ECO 3104 - Examples

This Version: September 26, 2013

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Supply and Demand

Problem 1:

The demand for books is: QD = 120− PThe supply of books is: QS = 5P

(a) What is the equilibrium price of books?

(b) What is the equilibrium quantity of books sold?

(c) If P = $15, do we observe a shortage or excess supply? How big is it?

(d) If P = $25, do we observe a shortage or excess supply? How big is it?

Problem 2:

The inverse demand curve for product X is given by:

PX = 25− 0.005Q+ 0.15PY ,

where PX represents price in dollars per unit, Q represents rate of sales inpounds per week, and PY represents selling price of another product Y indollars per unit. The inverse supply curve of product X is given by:

PX = 5 + 0.004Q.

Determine the equilibrium price and sales of X when the price of product Yis PY = $10.

Problem 3:

The daily demand for hotel rooms on Manhattan Island in New York is givenby the equation

QD = 250, 000− 375P.

The daily supply of hotel rooms on Manhattan Island is given by the equation

QS = 15, 000 + 212.5P.

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What is the equilibrium price and quantity of hotel rooms on ManhattanIsland?

Problem 4:

For U.S. consumers, the income elasticity of demand for fruit juice is 1.1. Theeconomy enters a recession and consumer income declines by 2.5%. What isthe expected percentage change in the quantity of fruit juice demanded?

Problem 5:

The cross-price elasticity of demand for peanut butter with respect to theprice of jelly is -0.3. The price of jelly declines by 15%.What is the expectedpercentage change in the quantity demanded for peanut butter?

Problem 6:

Harding Enterprises has developed a new product called the Gillooly Shille-lagh. The market demand for this product is given as follows:

Q = 240− 4P

(a) At what price is the price elasticity of demand equal to zero?

(b) At what price is demand infinitely elastic?

(c) At what price is the price elasticity of demand equal to minus one?

(d) If the shillelagh is priced at $40, what is the point price elasticity ofdemand?

Problem 7:

The demand for a bushel of wheat in 1981 was given by the equation

QD = 3550− 266P.

(a) What is the price elasticity of demand at a price of $3.46?

(b) If the price of wheat falls to $3.27 per bushel, what happens to therevenue generated from the sale of wheat?

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Consumer Behavior

Problem 8:

Consider Gary’s utility function: U(X, Y ) = 5XY , where X and Y are twogoods.

(a) If Gary consumed 10 units of X and received 250 units of utility, howmany units of Y must he have consumed?

(b) Would a market basket of X = 15 and Y = 3 be preferred to the abovecombination?

Problem 9:

A consumer has $100 per day to spend on product A, which has a unit priceof $7, and product B, which has a unit price of $15. What is the slope of thebudget line if good A is on the horizontal axis and good B is on the verticalaxis?

Problem 10:

If the quantity of good A (QA) is plotted along the horizontal axis, thequantity of good B (QB) is plotted along the vertical axis, the price of goodA is PA, the price of good B is PB and the consumer’s income is I, then theslope of the consumer’s budget constraint is .

Problem 11:

The budget constraint for a consumer who only buys apples (A) and bananas(B) is PAA + PBB = I where consumer income is I, the price of apples isPA, and the price of bananas is PB. To plot this budget constraint in a figurewith apples on the horizontal axis, we should use a budget line representedby which equation?

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Problem 12:

Sally consumes two goods, X and Y . Her utility function is given by theexpression U = 3XY 2. The current market price for X is $10, while themarket price for Y is $5. Sally’s current income is $500.

(a) Write the expression for Sally’s budget constraint.

(b) Determine the X, Y combination which maximizes Sally’s utility, givenher budget constraint.

(c) Calculate the impact on Sally’s optimum market basket of an increasein the price of X to $15. What would happen to her utility as a resultof the price increase?

Problem 13:

Jane lives in a dormitory that offers soft drinks and chips for sale in vendingmachines. Her utility function is U = 3SC (where S is the number of softdrinks per week and C the number of bags of chips per week), so her marginalutility of S is 3C and her marginal utility of C is 3S. Soft drinks are pricedat $0.50 each, chips $0.25 per bag.

(a) Write an expression for Jane’s marginal rate of substitution between softdrinks and chips.

(b) Use the expression generated in part (a) to determine Jane’s optimal mixof soft drinks and chips.

(c) If Jane has $5.00 per week to spend on chips and soft drinks, how manyof each should she purchase per week?

Problem 14:

An individual consumes products X and Y and spends $25 per time period.The prices of the two goods are $3 per unit for X and $2 per unit for Y . Theconsumer in this case has a utility function expressed as:

U(X, Y ) = 0.5XY

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(a) Express the budget equation mathematically.

(b) Determine the amount of consumption of X and Y that will maximizeutility.

(c) Determine the total utility that will be generated from the consumptionbundle you calculated in part (b).

Problem 15:

Janice Doe consumes two goods, X and Y . Janice has a utility functiongiven by the expression: U = 4X0.5Y 0.5. The current prices of X and Yare 25 and 50, respectively. Janice currently has an income of 750 per timeperiod.

(a) Calculate the Marginal Utility of X and Y

(b) Write an expression for Janice’s budget constraint.

(c) Calculate the optimal quantities of X and Y that Janice should choose,given her budget constraint.

(d) Suppose that the government rations purchases of good X such thatJanice is limited to 10 units of X per time period. Assuming that Janicechooses to spend her entire income, how much Y will Janice consume?

(e) Calculate the impact of the ration restriction on Janice’s utility.

Problem 16:

John consumes two goods, X and Y . The marginal utility of X and themarginal utility of Y satisfy the following equations:

MUX = Y and MUY = X.

The price of X is $9, and the price of Y is $12.

(a) Write an expression for John’s MRS.

(b) What is the optimal mix between X and Y in John’s market basket?

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(c) John is currently consuming 15 X and 10 Y per time period. Is heconsuming an optimal mix of X and Y ?

Problem 17:

Natasha derives utility from attending rock concerts (r) and from drinkingcolas (c) as follows:

U(c, r) = c0.9r0.1

(a) Calculate the marginal utility of cola (MUc) and the marginal utility ofrock concerts (MUr)

(b) If the price of cola (Pc) is $1 and the price of concert tickets (Pr) is$30 and Natasha’s income is $300, how many colas and tickets shouldNatasha buy to maximize utility?

(c) Suppose that the promoters of rock concerts require each fan to buy 4tickets or none at all. Under this constraint and given the above pricesand income, how many colas and tickets should Natasha buy to maximizeutility?

(d) Is Natasha better off with or without the constraint?

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Individual and Market Demand

Problem 18:

Donald derives utility from only two goods, carrots (Qc) and donuts (Qd).His utility function is as follows:

U(Qc, Qd) = QcQd

The marginal utility that Donald receives from carrots (MUc) and donuts(MUd) are given as follows:

MUc = Qd and MUd = Qc

Donald has an income (I) of $120 and the price of carrots (Pc) and donuts(Pd) are both $1.

(a) What is Donald’s budget line?

(b) What is the optimal ratio of Qc and Qd?

(c) What quantities of Qc and Qd will maximize Donald’s utility?

(d) Holding Donald’s income and Pd constant at $120 and $1 respectively,what is Donald’s demand curve for carrots?

(e) Suppose that a tax of $1 per unit is levied on donuts. How will this alterDonald’s utility maximizing market basket of goods?

Problem 19:

The following data pertain to products A and B, both of which are purchasedby Madame X. Initially, the prices of the products and quantities consumedare:

PA = $10, QA = 3, PB = $10, QB = 7.

Madame X has $100 to spend per time period. After a reduction in price ofB, the prices and quantities consumed are:

PA = $10, QA = 2.5, PB = $5, QB = 15.

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Assume that MadameX maximizes utility under both price conditions above.Also, note that if after the price reduction enough income were taken awayfrom Madame X to put her back on the original indifference curve, she wouldconsume this combination of A and B:

QA = 1.5, QB = 9

(a) Determine the change in consumption rate of good B due to (1) thesubstitution effect and (2) the income effect.

(b) Determine if product B is a normal, inferior, or Giffen good. Explain.

Problem 20:

A local retailer has decided to carry a well-known brand of shampoo. Themarketing department tells them that the quarterly demand by an averageman is:

QMd = 3− 0.25P

and the quarterly demand by an average woman is:

QWd = 4− 0.5P

The market consists of 10,000 men and 10,000 women. How may bottles ofshampoo can they expect to sell if they charge $6 per bottle?

Problem 21:

The price elasticity of demand for red herring is -4. The demand curve forred herring is: Q = 120− P . What is the price of red herring?

Problem 22:

Harding Enterprises has developed a new product called the Gillooly shille-lagh. The market demand for this product is given as follows:

Q = 240− 4P

(a) If the shillelagh is priced at $40, what is the price elasticity of demand?Is demand elastic or inelastic?

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(b) If the shillelagh price is increased slightly from $40, what will happen tothe total expenditure on the Gillooly shillelagh?

Problem 23:

The demand for telephone wire can be expressed as:

Q = 6000− 1, 500P,

where Q represents units, in pounds per day, and P represents price, indollars per pound. Determine the price elasticity of demand at P = $2.00per pound.

Problem 24:

The total world demand for power transmission wire is made up of bothdomestic and foreign demands. Thus, the total demand is the sum of thetwo sub-demands, which are given as:

Domestic demand:Pd = 5− 0.005Qd

Foreign demand:Pf = 3− 0.00075Qf ,

where Pd and Pf are in dollars per pound, and Qd and Qf are in pounds perday.

(a) Determine the total world demand for power transmission wire.

(b) Determine the prices at which domestic and foreign buyers would enterthe market.

(c) Determine the domestic and foreign quantities at P = $2.50 per pound.Check to see if the sum of Qd and Qf equals Q.

(d) Determine total quantity sold at P = $4.00 per pound.

Problem 25:

Suppose that the demand for artichokes (Qa) is given as:

Qa = 120− 4P

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(a) What is the price elasticity of demand if the price of artichokes is $10?

(b) Suppose that the price of artichokes increases to $12. What will happento the number of artichokes sold and the total expenditure by consumerson artichokes?

(c) At what price if any is the demand for artichokes infinitely elastic?

Problem 26:

Ronald’s monthly demand for Cap Rock Chardonnay is given by

Q = 6 +1

5, 000(I − T )− 1

10P,

where I is Ronald’s monthly income, T is his tax expense and P is the priceof Cap Rock Chardonnay. Suppose the price of Cap Rock Chardonnay is$10, Ronald’s monthly income is $15,000, and his tax expense is $5,000.

(a) How much does Ronald change his Chardonnay consumption if his taxesare increased by 20%.

(b) Calculate Ronald’s Consumer Surplus from consuming Cap Rock Chardon-nay before and after the increase in taxes.

Problem 27:

The wheat market is perfectly competitive, and the market supply and de-mand curves are given by the following equations:

QD = 20, 000, 000− 4, 000, 000P , and QS = 7, 000, 000 + 2, 500, 000P,

where QD and QS are quantity demanded and quantity supplied measuredin bushels, and P = price per bushel.

(a) Determine consumer surplus at the equilibrium price and quantity.

(b) Assume that the government has imposed a price floor at $2.25 per busheland agrees to buy any resulting excess supply. How many bushels ofwheat will the government be forced to buy? Determine consumer sur-plus with the price floor.

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Problem 28:

The market supply curve of rubber erasers is given by QS = 35, 000+2, 000P .The demand for rubber erasers can be segmented into two components. Thefirst component is the demand for rubber erasers by art students. Thisdemand is given by qA = 17, 000 − 250P . The second component is thedemand for rubber erasers by all others. This demand is given by qO =25, 000− 2000P .

(a) Derive the total market demand curve for rubber erasers.

(b) Find the equilibrium market price and quantity.

(c) Determine the consumer surplus for each component of demand.

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Production and the Cost of Production

Problem 29:

Joe owns a coffee house and produces coffee drinks under the productionfunction q = 5KL where q is the number of cups generated per hour, K isthe number of coffee machines (capital), and L is the number of employeeshired per hour (labor). What is the average product of labor?

Problem 30:

The total cost (TC) of producing computer software dvds (Q) is given as:TC = 200 + 5Q. What is the marginal cost?

Problem 31:

A firm’s total cost function is given by the equation:

TC = 4000 + 5Q+ 10Q2.

(a) Write an expression for each of the following cost concepts:

(i) Total Fixed Cost

(ii) Average Fixed Cost

(iii) Total Variable Cost

(iv) Average Variable Cost

(v) Marginal Cost

(b) Determine the quantity that minimizes average total cost.

Problem 32:

Acme Container Corporation produces egg cartons that are sold to egg dis-tributors. Acme has estimated this production function for its egg cartondivision:

Q = 25L0.6K0.4,

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where Q = output measured in one thousand carton lots, L = labor measuredin person hours, andK = capital measured in machine hours. Acme currentlypays a wage of $10 per hour and considers the relevant rental price for capitalto be $25 per hour. Determine the optimal capital-labor ratio that Acmeshould use in the egg carton division.

Problem 33:

Davy Metal Company produces brass fittings. Davy’s engineers estimate theproduction function represented below as relevant for their long-run capital-labor decisions.

Q = 500L0.6K0.8,

where Q = annual output measured in pounds, L =labor measured in personhours, K = capital measured in machine hours. The marginal products oflabor and capital are:

MPL = 300L−0.4K0.8, and MPK = 400L0.6K−0.2

Davy’s employees are relatively highly skilled and earn $15 per hour. Thefirm estimates a rental charge of $50 per hour on capital. Davy forecastsannual costs of $500,000 per year, measured in real dollars.

(a) Determine the firm’s optimal capital-labor ratio, given the informationabove.

(b) How much capital and labor should the firm employ, given the $500,000budget? Calculate the firm’s output.

(c) Davy is currently negotiating with a newly organized union. The firm’spersonnel manager indicates that the wage may rise to $22.50 under theproposed union contract. Analyze the effect of the higher union wage onthe optimal capital-labor ratio and the firm’s employment of capital andlabor. What will happen to the firm’s output?

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Problem 34:

The Longheel Press produces memo pads in its local shop. The company canrent its equipment and hire workers at competitive rates. Equipment neededfor this operation can be rented at $52 per hour, and labor can be hired at$12 per worker hour. The company has allocated $150,000 for the initial runof memo pads. The production function using available technology can beexpressed as:

Q = 0.25K0.25L0.75,

where Q represents memo pads (boxes per hour), K denotes capital input(units per hour), and L denotes labor input (units of worker time per hour).The marginal products of labor and capital are as follows:

MPL = (0.75)(0.25)K0.25L−0.25, and MPK = (0.25)(0.25)K−0.75L0.75

(a) Construct the isocost equation.

(b) Determine the appropriate input mix to get the greatest output for anoutlay of $150,000 for a production run of memo pads. Also, computethe level of output.

Problem 35:

A paper company dumps nondegradable waste into a river that flows by thefirm’s plant. The firm estimates its production function to be:

Q = 6KW,

where Q = annual paper production measured in pounds, K = machine hoursof capital, and W = gallons of polluted water dumped into the river per year.The marginal products of capital and waste generation are given as follows:

MPK = 6W , and MPW = 6K

The firm currently faces no environmental regulation in dumping waste intothe river. Without regulation, it costs the firm $7.50 per gallon dumped. Thefirm estimates a $30 per hour rental rate on capital. The operating budgetfor capital and waste water is $300,000 per year.

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(a) Determine the firm’s optimal ratio of waste water to capital.

(b) Given the firm’s $300,000 budget, how much capital and waste watershould the firm employ? How much output will the firm produce?

(c) The state environmental protection agency plans to impose a $7.50 efflu-ent fee for each gallon that is dumped. Assuming that the firm intendsto maintain its pre-fee output, how much capital and waste water shouldthe firm employ? How much will the firm pay in effluent fees? Whathappens to the firm’s cost as a result of the effluent fee?

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Profit Maximization and Competitive Supply

Problem 36:

Conigan Box Company produces cardboard boxes that are sold in bundles of1000 boxes. The market is highly competitive, with boxes currently sellingfor $100 per thousand. Conigan’s total cost curve is:

TC = 3, 000, 000 + 0.001Q2

where Q is measured in thousand box bundles per year.

(a) Calculate the marginal costs

(b) Calculate Conigan’s profit maximizing quantity. Is the firm earning aprofit?

(c) Analyze Conigan’s position in terms of the shutdown condition. ShouldConigan operate or shut down in the shortrun?

Problem 37:

Spacely Sprockets’ short-run cost curve is:

C(q,K) =25q2

K+ 15K,

where q is the number of Sprockets produced and K is the number of robothours Spacely hires. Currently, Spacely hires 10 robot hours per period. Theshort-run marginal cost curve is:

MC(q,K) = 50q

K.

Suppose the market is perfectly competitive. If Spacely receives $250 forevery sprocket he produces, what is his profit maximizing output level? Cal-culate Spacely’s profits.

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Problem 38:

Laura’s internet services has the following short-run cost curve:

C(q,K) =25q2

K2/3+ rK

where q is Laura’s output level, K is the number of servers she leases and ris the lease rate of servers. Laura’s short-run marginal cost function is:

MC(q,K) =50q

K2/3.

Currently, Laura leases 8 servers, the lease rate of servers is $15, and since themarket is perfectly competitive, Laura can sell all the output she producesfor $500 per unit.

(a) Find Laura’s short-run profit maximizing level of output. CalculateLaura’s profits.

(b) If the lease rate of internet servers rise to $20, how does Laura’s optimaloutput and profits change?

Problem 39:

Homer’s Boat Manufacturing cost function is: C(q) = 75128q4 +10, 240. Homer

can sell all the boats he produces for $1,200.

(a) What is the marginal cost function?

(b) What is his optimal output? Calculate Homer’s profit or loss.

Problem 40:

A competitive firm sells its product at a price of $0.10 per unit. Its total andmarginal cost functions are:

TC = 5− 0.05Q+ 0.001Q2

MC = −0.05 + 0.002Q,

where TC is total cost and Q is output rate (units per time period).

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(a) Determine the output rate that maximizes profit or minimizes losses inthe shortterm.

(b) If input prices increase and cause the cost functions to become

TC = 5− 0.10Q+ 0.002Q2

MC = −0.10 + 0.004Q,

what will the new equilibrium output rate be?

Problem 41:

Sarah’s Pretzel plant has the following short-run cost function:

C(q,K) =wq3

1000K3/2+ 50K

where q is Sarah’s output level, w is the cost of a labor hour, and K is thenumber of pretzel machines Sarah leases. Sarah’s short-run marginal costcurve is

MC(q,K) =3wq2

1000K3/2.

At the moment, Sarah leases 10 pretzel machines, the cost of a labor hour is$6.85, and she can sell all the output she produces at $35 per unit.

(a) Determine Sarah’s optimal output and profits.

(b) The cost per labor hour rises to $7.50, what happens to Sarah’s optimallevel of output and profits?

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Problem 42:

The market demand for a type of carpet known as KP-7 has been estimatedas:

P = 40− 0.25Q,

where P is price ($/yard) and Q is rate of sales (hundreds of yards permonth). The market supply is expressed as:

P = 5.0 + 0.05Q.

A typical firm in this market has a total cost function given as:

C = 100− 20.0q + 2.0q2.

where q is the output produced by the typical firm.

(a) Determine the equilibrium market output rate and price.

(b) Determine the output rate for a typical firm.

(c) Determine the rate of profit (or loss) earned by the typical firm.

Problem 43:

The market for wheat consists of 500 identical firms, each with the total andmarginal cost functions shown:

TC = 90, 000 + 0.00001q2

MC = 0.00002q,

where q is measured in bushels per year. The market demand curve forwheat is Q = 90, 000, 000 − 20, 000, 000P , where Q is the market quantitydemanded, again measured in bushels, and P is the price per bushel.

(a) Determine the short-run equilibrium price and quantity that would existin the market.

(b) Calculate the profit maximizing quantity for the individual firm. Calcu-late the firm’s short-run profit (loss) at that quantity.

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(c) Assume that the short-run profit or loss is representative of the currentlong-run prospects in this market. You may further assume that thereare no barriers to entry or exit in the market. Describe the expectedlong-run response to the conditions described in part b.

Problem 44:

Assume the market for tortillas is perfectly competitive. The market supplyand demand curves for tortillas are given as follows:

supply curve: P = .000002Q, demand curve: P = 11− .00002Q

The short run marginal cost curve for a typical tortilla factory is:

MC = .1 + .0009q

where q is the output for an individual firm, and Q is the market output.

(a) Determine the equilibrium price for tortillas.

(b) Determine the profit maximizing short run equilibrium level of outputfor a tortilla factory.

(c) Assuming that all of the tortilla factories are identical, how many tortillafactories are producing tortillas?

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The Analysis of Competitive Markets

Problem 45:

The utilities commission in a city is currently examining pay telephone servicein the city. The commission has been asked to evaluate a proposal by a citycouncil member to place a $0.10 price ceiling on local pay phone service. Thestaff economist at the utilities commission estimates the demand and supplycurves for pay telephone service as follows:

QD = 1600− 2400P , and QS = 200 + 3200P,

where P = price of a pay telephone call, and Q = number of pay telephonecalls per month.

(a) Determine the equilibrium price and quantity that will prevail withoutthe price ceiling.

(b) Analyze the quantity that will be available with the price ceiling.

Problem 46:

In a competitive market, the following supply and demand equations aregiven:

Supply P = 5 + 0.036Q, and Demand P = 100− 0.04Q,

where P represents price per unit in dollars, and Q represents rate of salesin units per year.

(a) Determine the equilibrium price and sales rate.

(b) Determine the deadweight loss that would result if the government wereto impose a price ceiling of 40 dollars per unit.

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Problem 47:

The demand and supply functions for basic cable TV in the local market aregiven as:

QD = 200, 000− 4, 000P and QS = 20, 000 + 2, 000P.

(a) Calculate the consumer and producer surplus in this market.

(b) If the government implements a price ceiling of $15 on the price of basiccable service, calculate the new levels of consumer and producer surplus.Are all consumers better off? Are producers better off?

Problem 48:

The market demand and supply functions for pork are:

QD = 2, 000− 500P and QS = 800 + 100P.

To help pork producers, the U.S. Congress is considering legislation thatwould put a price floor at $2.25 per unit. To achieve this price floor thegovernment wants to buy enough units of pork to keep the price at $2.25 perunit.

(a) How many units of pork will the government be forced to buy to keepthe price at $2.25?

(b) How much will the government spend in total?

(c) How much does producer surplus increase?

Problem 49:

The market demand and supply functions for milk are:

QD = 58− 30.4P and QS = 16 + 3.2P.

To help milk producers the government considers implementing a price floorof $1.75 and the government will purchase all the excess units at $1.75.

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(a) How does the price floor affect the producer surplus? Calculate thechange in producer surplus.

(b) How many surplus units of milk are being produced?

(c) What are the milk expenditures of the government?

(d) Does the increase in producer surplus due to the price floor exceed gov-ernment spending on excess milk?

Problem 50:

The market for semiskilled labor can be represented by the following supplyand demand curves:

LD = 32000− 4000W and LS = −8000 + 6000W,

where L = millions of person hours per year, and W = the wage in dollarsper hour.

(a) Calculate the equilibrium price and quantity that would exist under afree market.

(b) What impact does a minimum wage of $3.35 per hour have on the mar-ket?

(c) The government is contemplating an increase in the minimum wage to$5.00 per hour. Calculate the impact of the new minimum wage on thequantity of labor supplied and demanded.

(d) Calculate producer surplus (laborers’ surplus) before and after the pro-posed change.

Problem 51:

The supply and demand curves for corn are as follows:

QD = 3, 750− 725P and QS = 920 + 690P,

where Q = millions of bushels and P = price per bushel.

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(a) Calculate the equilibrium price and quantity that would prevail in thefree market.

(b) The government has imposed a $2.50 per bushel support price. Howmuch corn will the government be forced to purchase?

(c) Calculate the loss in consumer surplus that would occur under the sup-port program.

Problem 52:

The market for all-leather men’s shoes is served by both domestic (U.S.)and foreign (F) producers. The domestic producers have been complainingthat foreign producers are dumping shoes onto the U.S. market. As a result,Congress is very close to enacting a policy that would completely prohibitsales by foreign manufacturers of leather shoes in the U.S. market. Thedemand curve and relevant supply curves for the leather shoe market are asfollows:

QD = 50, 000− 500P

QSUS = 6000 + 150P

QSF = 2000 + 50P,

where Q = thousands of pairs of shoes per year, and P = price per pair.

(a) Currently there are no restrictions covering all-leather men’s shoes. Whatare the current equilibrium values?

(b) Calculate the price and quantity that would prevail if the proposed policyis enacted.

Problem 53:

The market demand and supply functions for imported cars are:

QD = 800, 000− 5P and QS = (14 +1

6)P + 225, 000.

The legislature is considering a tariff (a tax on imported goods) equal to$2,000 per unit to aid domestic car manufacturers.

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(a) What is the producer surplus if the tariff is implemented?

(b) How many cars are imported?

(c) Suppose that instead of a tariff, importers agree to voluntarily restricttheir imports to this level. If they do and no tariff is implemented,calculate producer surplus in this scenario.

(d) Do you expect importers will be more in favor of a tariff or a voluntaryquota?

Problem 54:

A country which does not tax cigarettes is considering the introduction ofa $0.40 per pack tax. The economic advisors to the country estimate thesupply and demand curves for cigarettes as:

QD = 140, 000− 25, 000P and QS = 20, 000 + 75, 000P,

where Q = daily sales in packs of cigarettes, and P = price per pack. Thecountry has hired you to provide the following information regarding thecigarette market and the proposed tax.

(a) What are the equilibrium values in the current environment with no tax?

(b) What price and quantity would prevail after the imposition of the tax?What portion of the tax would be borne by buyers and sellers respec-tively?

(c) Calculate the deadweight loss from the tax. What is the revenue fromthe tax?

Problem 55:

The market demand and supply functions for cotton are:

QD = 10− 0.04P and QS = 38P − 20.

(a) Calculate the consumer and producer surplus.

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(b) To assist cotton farmers, suppose a subsidy of $0.10 a unit is imple-mented. Calculate the new level of consumer and producer surplus.

(c) Did the increase in consumer and producer surplus exceed the increasedgovernment spending necessary to finance the subsidy?

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Market Power: Monopoly

Problem 56:

Barbara is a producer in a monopoly industry. Her demand curve, total rev-enue curve, marginal revenue curve and total cost curve are given as follows:

Q = 160− 4P ; TR = 40Q− 0.25Q2

MR = 40− 0.5Q; TC = 4Q; MC = 4

(a) How much output will Barbara produce?

(b) What is the price of her product?

(c) How much profit will she make?

Problem 57:

A monopolist faces the following demand curve, marginal revenue curve, totalcost curve and marginal cost curve for its product:

Q = 200− 2P ; MR = 100−Q

TC = 5Q; MC = 5

(a) What level of output maximizes total revenue?

(b) What is the profit maximizing level of output?

(c) What is the profit maximizing price?

(d) How much profit does the monopolist earn?

Problem 58:

The marginal revenue of green ink pads is given as follows:

MR = 2500− 5Q

The marginal cost of green ink pads is 5Q.

28

(a) How many ink pads will be produced to maximize revenue?

(b) How many ink pads will be produced to maximize profit?

Problem 59:

The marginal cost of a monopolist is constant and is $10. The marginalrevenue curve is given as follows:

MR = 100− 2Q

What is the profit maximizing price?

Problem 60:

A firm’s demand curve is given by

P = 500− 2Q.

The firm’s current price is $300 and the firm sells 100 units of output perweek.

(a) Calculate the firm’s marginal revenue at the current price and quantityusing the expression for marginal revenue that utilizes the price elasticityof demand.

(b) Assuming that the firm’s marginal cost is zero, is the firm maximizingprofit?

Problem 61:

The marginal cost of a monopolist is constant and is $10. The demand curveand marginal revenue curves are given as follows:

Q = 100− P ; MR = 100− 2Q

What is the deadweight loss from monopoly power?

29

Problem 62:

Determine the rule-of-thumb price, when the monopolist has a marginal costof $25 and the price elasticity of demand is -3.0

Problem 63:

Maui Macadamia Inc. has a monopoly in the macadamia nut industry. Thedemand curve, marginal revenue and marginal cost curve for macadamia nutsare given as follows:

P = 360− 4Q; MR = 360− 8Q; MC = 4Q

(a) What level of output maximizes the sum of consumer surplus and pro-ducer surplus?

(b) What is the profit maximizing level of output?

(c) At the profit maximizing level of output, what is the level of consumersurplus?

(d) At the profit maximizing level of output, what is the level of producersurplus?

(e) At the profit maximizing level of output, what is the deadweight loss?

30

Problem 64:

John Gardner is the city planner in a medium-sized southeastern city. Thecity is considering a proposal to award an exclusive contract to Clear Vision,Inc., a cable television carrier. Mr. Gardner has discovered that an economicplanner hired a year before has generated the demand, marginal revenue, andmarginal cost functions given below:

P = 28− 0.0008Q; MR = 28− 0.0016Q

MC = 0.0012Q,

where Q = the number of cable subscribers and P = the price of basicmonthly cable service. Conditions change very slowly in the community sothat Mr. Gardner considers the cost and demand functions to be reasonablyvalid for present conditions. Mr. Gardner knows relatively little economicsand has hired you to answer the questions listed below.

(a) What price and quantity would be expected if the firm is allowed tooperate completely unregulated?

(b) Mr. Gardner has asked you to recommend a price and quantity thatwould be socially efficient. Recommend a price and quantity to Mr.Gardner using economic theory to justify your answer.

(c) Compare the economic efficiency implications of (a) and (b) above.

31

Pricing with Market Power

Problem 65:

A firm sells an identical product to two groups of consumers, A and B. Thefirm has decided that third-degree price discrimination is feasible and wishesto set prices that maximize profits. Which price and output strategy willmaximize profits?

Problem 66:

Calloway Shirt Manufacturers sells knit shirts in two sub-markets. In onesub-market, the shirts carry Calloway’s popular label and breast logo and re-ceive a substantial price premium. The other sub-market is targeted towardmore price conscious consumers who buy the shirts without a breast logo,and the shirts are labeled with the name Archwood. The retail price of theshirts carrying the Calloway label is $42.00 while the Archwood shirts sellfor $25. Calloway’s market research indicates a price elasticity of demandfor the higher priced shirt of -2.0, and the elasticity of demand for the Arch-wood shirts is -4.0. Moreover, the research suggests that both elasticities areconstant over broad ranges of output.

(a) Are Calloway’s current prices optimal?

(b) Management considers the $25 price to be optimal and necessary to meetthe competition. What price should the firm set for the Calloway labelto achieve an optimal price ratio?

Problem 67:

American Tire and Rubber Company sells identical radial tires under thefirm’s own brand name and private label tires to discount stores. The radialtires sold in both sub-markets are identical, and the marginal cost is constantat $10 per tire for both types. The firm has estimated the following demandcurves for each of the markets.

PB = 70− 0.0005QB(brand name)

32

PP = 20− 0.0002QP (private label).

Quantities are measured in thousands per month and price refers to thewholesale price. American currently sells brand name tires at a wholesaleprice of $28.50 and private label tires for a price of $17. Are these pricesoptimal for the firm?

Problem 68:

A lower east-side cinema charges $3.00 per ticket for children under 12 yearsof age and $5.00 per ticket for anyone 12 years of age or older. The firm hasestimated that the price elasticity of demand for tickets purchased by those12 years of age or older is -1.5. Calculate the elasticity of demand for ticketspurchased for children under 12 years of age if prices are optimal.

Problem 69:

The local zoo has hired you to assist them in setting admission prices. Thezoo’s managers recognize that there are two distinct demand curves for zooadmission. One demand curve applies to those ages 12 to 64, while the otheris for children and senior citizens. The two demand and marginal revenuecurves are:

PA = 9.6− 0.08QA; MRA = 9.6− 0.16QA

PC/S = 4− 0.05QCS; MRC/S = 4− 0.10QCS

where PA = adult price, PC/S = children’s/senior citizen’s price, QA = dailyquantity of adults, and QC/S = daily quantity of children and senior citizens.Crowding is not a problem at the zoo, so that the managers consider marginalcost to be zero. If the zoo decides to price discriminate, what are the profitmaximizing price and quantity in each market? Calculate total revenue ineach sub-market.

33

Problem 70:

The BCY Corporation provides accounting services to a wide variety of cus-tomers, most of whom have had a business association with BCY for morethan five years. BCY’s demand and marginal revenue curves are:

P = 10, 000− 10Q; MR = 10, 000− 20Q.

BCY’s marginal cost of service is: MC = 5Q.

(a) If BCY charges a uniform price for a unit of accounting service, Q, whatprice must it charge per unit, and how many units must it produce pertime period in order to maximize profit? Calculate the consumer surplus.

(b) If BCY could enforce first-degree price discrimination, what would be thelowest price that it would charge and how many units would it produceper time period?

(c) With perfect price discrimination and ignoring any fixed cost, what is to-tal profit? How much additional consumer surplus is captured by switch-ing from a uniform price to first-degree price discrimination?

Problem 71:

The industry demand curve for a particular market is:

Q = 1800− 200P.

The industry exhibits constant long-run average cost at all levels of output,regardless of the market structure. Long-run average cost is a constant $1.50per unit of output. Compare the economic efficiency of each possibility.

(a) Calculate market output, price (if applicable), consumer surplus, andproducer surplus (profit) for each of the scenarios below.

(i) Perfect Competition

(ii) Pure Monopoly (Hint: MR = 9− 0.01Q)

(iii) First Degree Price Discrimination

(b) Compare the economic efficiency of each scenario.

34

Monopolistic Competition & Oligopoly

Problem 72:

A firm operating in a monopolistically competitive market faces the followingdemand curve:

P = 10− 0.1Q

The firm’s total and marginal cost curves are:

C = −10Q+ 0.15Q2 + 130 and MC = −10 + 0.3Q,

where P is in dollars per unit, output rate Q is in units per time period, andtotal cost C is in dollars.

(a) From the demand curve facing the firm, determine the firm’s MarginalRevenue equation.

(b) Determine the price and output rate that will allow the firm to maximizeprofit or minimize losses.

(c) Compute a Lerner index for the firm.

Problem 73:

The local pizza market is monopolistically competitive. One of the localproducers in the market is a pizza place called One Guy’s Pizza. The demandequation facing One Guy’s Pizza is given by

Qd = 225− 10P

or equivalently,P = 22.5− 0.1Qd.

One Guy’s Pizza has a cost function equal to:

C(Q) = 0.15Q2

(a) What is the marginal revenue curve for One Guy’s Pizza?

35

(b) What is the marginal cost for One Guy’s Pizza?

(c) Determine the profit maximizing level of output and the price chargedto customers by One Guy’s Pizza.

(d) Would you expect the price and output to be the same in a long-runequilibrium?

Problem 74:

Suppose that the market demand for mountain spring water is given as fol-lows:

P = 1200−Q

Mountain spring water can be produced at no cost (i.e. TC = MC = 0).

(a) What is the profit maximizing level of output and price of a monopolist?

(b) What level of output would be produced by each firm in a Cournotduopoly equilibrium? What will be the equilibrium price?

(c) What would be the equilibrium level of output and price in the long runif the industry was perfectly competitive?

Problem 75:

Two large diversified consumer products firms are about to enter the marketfor a new pain reliever. The two firms (Firm A and Firm B) are very similarin terms of their costs, strategic approach, and market outlook. Moreover, thefirms have very similar individual demand curves so that each firm expectsto sell one-half of the total market output at any given price. The marketdemand curve for the pain reliever is given as:

Q = 2600− 400P.

Both firms have constant long-run average costs of $2.00 per bottle. Patentprotection insures that the two firms will operate as a duopoly for the fore-seeable future. Price and quantity values are stated in per-bottle terms. Ifthe firms act as Cournot duopolists, solve for

36

(a) Firm A’s reaction curve;

(b) Firm B’s reaction curve;

(c) The Cournot equilibrium quantities and price.

Problem 76:

Consider two identical firms (Firm 1 and Firm 2) that face a linear marketdemand curve. Each firm has a marginal cost of zero and the two firmstogether face demand:

P = 50− 0.5Q,

where Q = Q1 +Q2.

(a) Find the Cournot equilibrium Q1, Q2 and P .

(b) Find the equilibrium Q and P for each firm assuming that the firmscollude and share the profit equally.

(c) Compare the efficiency of the equilibrium outcomes derived in (a) and(b) above.

Problem 77:

The Grand River Brick Corporation (Firm G) uses Business-to-Business in-ternet technology to set output before Bernard’s Bricks (Firm B). This givesthe Grand River Brick Corporation ”first-move” ability. The market demandfor bricks is

Q = 1, 000− 100P or P = 10− 0.01Q.

Total output is Q = (qB +qG), where qB is the output produced by Bernard’sBricks and qG is the output produced by Grand River Brick Corporation. Themarginal cost of producing an additional unit of bricks is constant at $2.00for each firm.

(a) Determine the reaction curve for Bernard’s Bricks.

(b) Given that the Grand River Brick Corporation has this information andmoves first, determine the optimal output decision for Grand River BrickCorporation.

37

(c) Does the ”first-move” ability of the Grand River Brick Corporation allowthem to capture a larger market share?

38

Solutions

39

Supply and Demand

Problem 1:

(a) 20

(b) 100

(c) Shortage equal to 30

(d) Excess supply equal to 30

Problem 2:Q = 2, 388.9 units per week; P = $14.56 per unit.

Problem 3:Q = 100, 000; P = $400

Problem 4:−2.75%

Problem 5:4.5%

Problem 6:

(a) The price elasticity of demand equals zero (is completely inelastic) at aprice of zero.

(b) Demand is infinitely elastic at a price of $60.

(c) At a price of $30.

(d) The price elasticity of demand equals PQ

∆Q∆P

= −2.

Problem 7:

(a) PQ

∆Q∆P

= −0.35

(b) The revenue drops by $334.36.

40

Consumer Behavior

Problem 8:

(a) Y = 5

(b) The first combination would be preferred as it leads to higher units ofutility.

Problem 9:−7/15

Problem 10:−PA

PB

Problem 11:B = I

PB− PA

PBA

Problem 12:

(a) 500 = 10X + 5Y

(b) X = 16.67 and Y = 66.67

(c) X = 11.11 and Y = 66.67. Utility declines by roughly 74,141 units.

Problem 13:

(a) MRS = MUS

MUC= 3C

3S= C

S

(b) MRS = PS

PC⇒ C

S= 0.5

0.25= 1

2Jane should by twice as many chips as soft

drinks

(c) Jane should spend her $5.00 to buy 5 soft drinks and 10 bags of chips.

Problem 14:

(a) I = PXX + PY Y ⇒ 25 = 3X + 2Y

(b) X = 4.17 and Y = 6.25

41

(c) 13.03 units of utility per time period.

Problem 15:

(a) MUX = 2Y 0.5

X0.5 and MUY = 2X0.5

Y 0.5

(b) 750 = 25X + 50Y

(c) X = 15 and Y = 7.5

(d) X = 10 and Y = 10

(e) U(X=15,Y =7.5) = 42.43 and U(X=10,Y =10) = 40. Utility declines.

Problem 16:

(a) MRS = MUX

MUY= Y

X

(b) MRS = PX

PY⇒ Y

X= 9

12= 0.75

(c) No, the mix is not optimal. He should consume 0.75 times as much Y asX, rather than his current 0.67 Y for each X

Problem 17:

(a) MUc = 0.9c−0.1r0.1 and MUr = 0.1c0.9r−0.9

(b) c = 270 and r = 1

(c) U(c=300,r=0) = 0 and U(c=180,r=4) = 123.01. Natasha is better off withbuying the four tickets.

(d) U(c=270,r=1) = 154.25 > 123.01 = U(c=180,r=4). Natasha would have ahigher utility without the constrain. Constraining choices of fully ratio-nal actors always leads to lower utilities.

42

Individual and Market Demand

Problem 18:

(a) Budget line: 120 = Qc +Qd

(b) Qc

Qd= 1 or Qc = Qd

(c) Qc = 60 and Qd = 60

(d) Qc = 120Pc+1

(e) Qd = 30 and Qc = 60

Problem 19:

(a) The total effect of the price change is the difference in quantities beforeand after the price change. This change includes income and substitutioneffects. The reduction in consumption that resulted from the reductionin income to put Madame X back on the original indifference curve rep-resents the income effect. The difference between the total effect and theincome effect is the substitution effect.Total effect: 15− 7 = 8Income effect: 15− 9 = 6Substitution effect: (15− 7)− (15− 9) = 2

(b) Substitution and income effect are additive and both positive (6+2 = 8).Thus, we have a normal good.

Problem 20:25,000 bottles

Problem 21:P = $96

Problem 22:

(a) E = 4080

(−4) = −2 and demand is elastic.

43

(b) If the price of a good with elastic demand is increased, the total expen-ditures on the good will decrease (the percentage decrease of demand isbigger than the percentage increase of the price).

Problem 23:

(a) E = −1, unitary elasticity at this price.

Problem 24:

(a) Q =

0 ,if P ≥ 5

1000− 200P ,if 5 ≥ P ≥ 3

5000− 1533.33P ,if 3 ≥ P

(b) Domestic buyers at P ≤ 5Foreign buyers at P ≤ 3.

(c) Qd(P = 2.5) = 500.00Qf (P = 2.5) = 666.68Q(P = 2.5) = 1, 166.68Check Q = Qd +Qf = 500.00 + 666.68 = 1, 166.68

(d) Only domestic demand for this price: Q = 200

Problem 25:

(a) E = −0.5

(b) TE = P ∗Q. Total expenditures increase from $800 to $864, even thoughthe total number of artichokes sold has fallen from 80 to 72.

(c) Demand is infinitely elastic at the price where the demand curve inter-sects the vertical y-axis. Here, this occurs at P = $30

Problem 26:

(a) Consumption falls from Q(T=5,000)=7 to Q(T=6,000)=6.8 by 0.2

44

(b) The choke price with the old tax is P = $80.His consumer surplus is 0.5($80− $10)7 = $245.The choke price after the tax increase is P = $78.His consumer surplus decreases to 0.5($78− $10)6.8 = $231.2.

Problem 27:

(a) CS = 0.5(5− 2)12, 000, 000 = 18, 000, 000

(b) Government would have to by the whole excess supply:QS −QD = 1, 625, 000CS = 0.5(5− 2.25)11, 000, 000 = 15, 125, 000

Problem 28:

(a) Q =

0 ,if P ≥ 68

17, 000− 250P ,if 68 > P ≥ 12.5

42, 000− 2, 250P ,if 12.5 > P

(b) Check if an equilibrium exists at a price at which art students and othersbuy rubbers: 42, 000− 2, 250P = 35, 000 + 2, 000PIt does exists; P ∗ = 1.65 and Q∗ = 38, 287.5

(c) CSA = 0.5(68− 1.65)16, 587.5 = $550, 290.31CSO = 0.5(12.5− 1.65)21, 700 = $117, 722.5

45

Production and the Cost of Production

Problem 29:APLabor = q

L= 5KL

L= 5K

Problem 30:∆TC∆Q

= 5

Problem 31:

(a) (i) TFC = 4000

(ii) AFC = 4000Q

(iii) TV C = TC − TFC = 5Q+ 10Q2

(iv) AV C = TV CQ

= 5 + 10Q

(v) ATC = TCQ

= 4000+5Q+10Q2

Q

(vi) MC = ∆TC∆Q

= 5 + 20Q

(b) MC = ATC ⇒ Q = 20

Problem 32:MRTS = MPL

MPKand MRTS = w

r

1.5KL

= 1025⇒ 1.5K = 0.4L⇒ K = 0.266L

Problem 33:

(a) 0.75KL

= 1550⇒ K

L= 0.4⇒ K = 0.4L

(b) Hint:C = wL + rK; insert wage, rent charge, and the ratio from (a)L ≈ 14, 286 hours; K ≈ 5, 714 and Q ≈ 157, 568, 202.

(c) Hint: MRTS = 0.75KL

; new input price ratio: 22.550

New optimal capital-labor ratio: K = 0.6LAmount of labor is reduced (L ≈ 9, 524), amount of capital remainsconstant (K ≈ 5, 714) and output is reduced (Q ≈ 123, 541, 772)

46

Problem 34:

(a) I = wL+ rK ⇒ 150, 000 = 12L+ 52K

(b) L = 9, 375, K = 721.15, Q = 1, 234.29

Problem 35:

(a) KW

= 0.25 or K = 0.25W

(b) W = 20, 000, K = 5, 000 and Q = 600, 000, 000

(c) W ≈ 14, 142, K ≈ 7, 071Cost for effluent fees F = 106, 065. The costs rises from $300,000 to$424,260 (C = PWW + PKK with PW including the the fee)

Profit Maximization and Competitive Supply

Problem 36:

(a) MC = 0.002Q

(b) Q = 50, 000 and π = −$500, 000

(c) Firm should operate since P > AV C

Problem 37:q = 50 and π = 6, 100

Problem 38:

(a) q = 40 and π = 9, 880

(b) Short-run output is unaffected q = 40 and profit is reduced to π = 9, 840

47

Problem 39:

(a) MC = 7532q3

(b) q = 3√

512 = 8 and π = −$3, 040Homer will produce and make a loss, because P > AV C(8). Producingand loosing $3,040 is better than not producing and losing $10,240.

Problem 40:

(a) Q = 75

(b) Q = 50

Problem 41:

(a) Q = 232.07 and π = 4, 915.08

(b) Optimal output and profit falls:Q = 221.79 and π = 4, 675.11

Problem 42:

(a) Q = 116.7 and P = 10.825

(b) q = 7.71

(c) π = 18.77

Problem 43:

(a) P = 2 and Q = 50, 000, 000

(b) Q = 100, 000 and π = 10, 000

48

(c) Firms are earning an economic profit so we would expect other firms tojoin this market (supply curve shifts rightwards). The price would fallcausing the firms to reduce their outputs. This will continue until wereach the long-term equilibrium with zero profits.

Problem 44:

(a) Q = 500, 000 and P = 1

(b) q = 1, 000

(c) Since Q = 500, 000 and q = 1, 000 there must be 500 firms.

49

The Analysis of Competitive Markets

Problem 45:

(a) P = 0.25 and Q = 1, 000

(b) QS = 520 and QD = 1360. We observe a shortage of 840 calls.

Problem 46:

(a) Q = 1, 250 and P = $50

(b) Deadweight loss 0.5(61.11− 40)(1250− 972.22) = 2, 931.97

Problem 47:

(a) P ∗ = $30, Q∗ = 80, 000, PC = $50, QS(P=0) = 20, 000CS = 0.5(50− 30)80, 000 = $800, 000PS = 30 · 20, 000 + 0.5(80, 000− 20, 000)30 = $1, 500, 000

(b) QS(P=15) = 50, 000CS = 0.5(50− 37.5)50, 000 + 50, 000(37.5− 15) = $1, 437, 500PS = 15 · 20, 000 + 0.5(50, 000− 20, 000)15 = $525, 000Consumer surplus increases, but producers surplus decreases. Not allconsumers are better off: some would be willing to pay $15, but becauseof the shortage they are unable to get cable TV.

Problem 48:

(a) Government will be forced to buy 150 units of pork

(b) Government spending: 150 ∗ 2.25 = 337.5

50

(c) QS(P=0) = 800PS∗ = 800 · 2 + 0.5(1, 000− 800)2 = $1, 800PS ′ = 800 · 2.25 + 0.5(1, 025− 800)2.25 = $2, 053.125∆PS = PS ′ − PS∗ = $253.125

Problem 49:

(a) PS∗ = $22.5, PS ′ = $32.9, ∆PS = PS ′ − PS∗ = $10.4

(b) Q′S = 21.6, Q′D = 4.8, Excess supply of 16.8

(c) Government spending 16.8 ∗ 1.75 = $29.4The increase in producer surplus does not exceed the government spend-ings

Problem 50:

(a) W ∗ = $4, Q∗ = $16, 000

(b) A minimum wage of 3.35 would be below the equilibrium wage and wouldnot be binding. Thus, the market would attain its free market equilib-rium.

(c) LD = 12, 000, and LS = 22, 000. The new minimum wage would createunemployment 0f 10,000 person hours per year.

(d) Hint: For W = 0 we would have a negative supply of labor (LS). Thus,instead of searching for LS(W=0) we search for a wage where LS = 0(reservation price). Try to graph LS if you have problems understandingthis pointPS∗ = 0.5(4− 1.33)16, 000 = $21, 360For which wage would workers supply the demanded quantity of work:W = 1.33 + 0.000167LS = 3.33PS ′ = 0.5(3.33− 1.33)12, 000 + (5− 3.33)12, 000 = $32, 040Overall producer surplus has increased, but single workers might be worseof because of the increased unemployment rate.

51

Problem 51:

(a) P ∗ = 2 and Q∗ = 2, 300

(b) QS = 2, 645 and QD = 1937.5 Government would have to buy the differ-ence of 707.5 millions bushels.

(c) ∆CS ≈ −1, 059

Problem 52:

(a) P ∗ = 60 and Q∗ = 20, 000

(b) P ′ = 67.69 and Q′ = 16, 155

Problem 53:

(a) PS∗ = PS ′ = 225, 000(31, 478.26−2, 000)+0.5(642, 608.7−225, 000)(31, 478.26−2, 000) = $12, 787, 797, 732

(b) Q = 42, 608.7

(c) PS ′′ = 225, 000(31, 478.26) + 0.5(642, 608.7 − 225, 000)(31, 478.26) =$13, 655, 406, 427

(d) They will favor the voluntary quota. They can sell the same amount ofcars but receive the full price instead the price minus the tariff.

Problem 54:

(a) P = 1.2 and Q = 110, 000

(b) Four conditions must hold:QD = 140, 000− 25, 000PB

QS = 20, 000 + 75, 000PS

QD = QS

52

PB = PS + 0.4In equilibrium: 140, 000− 25, 000PB = 20, 000 + 75, 000PS

Hint: Substituting for PB

PS = 1.10, PB = 1.50, Q = 102, 500The tax is paid $0.3 by buyers (P = 1.2⇒ PB = 1.5) and $0.1 by sellers(P = 1.2⇒ PS = 1.1)

(c) Area A: (110, 000− 102, 500)(1.5− 1.2)0.5 = 1, 125Area B: (110, 000− 102, 500)(1.2− 1.1)0.5 = 375Deadweight Loss: $1500Revenue from tax: 0.4 ∗ 102, 500 = $41, 000 per day

Problem 55:

(a) P = 0.79, Q = 9.97, choke price PC = 250, reservation price PR = 0.53CS = 0.5(250− 0.79)9.97 = $1, 242.31PS = 0.5(0.79− 0.53)9.97 = $1.30

(b) New equilibrium if: 10− 0.04P = 38(P + 0.1)− 20P = 0.69, QS = 9.97CS = 0.5(250− 0.69)9.97 = $1, 242.81PS = 0.5(0.79− 0.53)9.97 = $1.30

(c) Government spending is $0.997. The increase in consumer surplus is$.50, the producer surplus did not change. The increase in consumerand producer surplus is less than government spending.

53

Market Power: Monopoly

Problem 56:

(a) Q = 72

(b) P = 22

(c) π = 1, 296

Problem 57:

(a) Q = 100

(b) Q = 95

(c) P = $52.5

(d) π = $4, 512.5

Problem 58:

(a) Q = 500

(b) Q = 250

Problem 59:p = $55

Problem 60:

(a) ED = −1.5MR = P + P 1

ED= 100

(b) MR = MC thus the quantity should be Q = 125. Firm sells less than125 and is not maximizing the profit.

54

Problem 61:

Deadweight loss from monopoly power is $1,012.5

Problem 62:

P = MC1+ 1

ED

= $37.5

Problem 63:

(a) Q = 45

(b) Q = 30

(c) CS = $1, 800

(d) PS = $5, 400

(e) $900

Problem 64:

(a) Q = 10, 000 and P = $20

(b) Q = 14, 000 and P = $16.8

(c) If the profit maximizing quantity is produced the deadweight loss frommonopoly power is $16,000

55

Pricing with Market Power

Problem 65:

MRA = MRB = MC

Problem 66:

(a) PC

PA= 1.68, but 1+(1/EA)

1+(1/EC)= 1.5. Thus current prices are not optimal.

(b) PC

PAshould be 1.5. Given PA = $25, PC should be $37.5

Problem 67:

Prices should be PB = $40 and PP = $15. Thus, prices are not optimal.

Problem 68:

EChild = −2.25

Problem 69:

QA = 60, PA = $4.8QCS = 40, PCS = $2TRA = $288, TRCS = $368

Problem 70:

(a) Q∗ = 400 and P ∗ = $6, 000CS = 0.5(10, 000− 6000)400 = $800, 000

(b) Lowest price would occur if MC=ARQ = 666.67 and P$3, 333.33

(c) π = $3, 333, 353.33Loss in consumer surplus due to first-degree price discrimination is $800,000.Everything from answer (a).

56

Problem 71:

Hint: Since LAC is constant, LMC is also constant and equal to LAC.LMC = $1.5

(a) (i) Q = 1, 500, P = LAC, PS = $0,CS = 0.5(9− 1.5)1500 = $5, 625

(ii) Q = 750, P = $5.25, PS = $2812.5,CS = 0.5(9− 5.25)750 = $4, 218.75

(iii) Q = 1, 500, PS = $5, 625, CS = $0

(b) Comparison of Efficiency:

(i) Competition: CS+PS = $5,625

(ii) Monopoly: CS+PS = $4,218.75

(iii) First Degree: CS+PS = $5,625

Monopoly results in a deadweight loss. First-degree price discriminationresults in a redistribution of income, but does not change the overallwelfare.

Problem 72:

(a) MR = 10− 0.2Q

(b) Q∗ = 40 and P ∗ = 6

(c) L = 23

Problem 73:

(a) MR = 22.5− 0.2Qd

(b) MC = 0.3Q

(c) Q∗ = 45 and P ∗ = 18

(d) No. The profit for One Guy’s Pizza is π = 506.25, which suggests thatother firms will want to enter the market and in the long-run, otherfirms will enter, demand will shift away from One Guy’s Pizza, and theirprofits will fall to zero.

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Problem 74:

(a) Q = 600 and P = 600

(b) Q1 = Q2 = 400. Thus the total output is 800 and the price will beP = $400.

(c) Q = 1, 200 and P = 0

Problem 75:

(a) QA = 900− 0.5QB

(b) QB = 900− 0.5QA

(c) QA = 600 and QB = 600, while P = $3.50

Problem 76:

(a) Q1 = Q2 = 33.33 and P = 16.66.

(b) Q = 50 and if profits are shared equally, Q1 = Q2 = 25. Then P = 25.

(c) Both cases result in inefficiency. However, the inefficiency (deadweightloss) is smaller when the firms compete with each other. When theycollude, output is restricted even further and price is significantly higherthan marginal cost (which is zero in this case).

Problem 77:

(a) QB = 400− 0.5QG

(b) QG = 400. Therefore, QB = 200.

(c) If Grand River Brick Corporation did not have first-mover ability, theoutcome would be the Cournot equilibrium, which is QG = QB = 266.66.Thus, first-mover ability has given Grand River a greater market share.

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