ECO 100Y – L0201 A INTRODUCTION TO ECONOMICS Take-Home...

Department of Economics Prof. Gustavo Indart University of Toronto July 18, 2006 ECO 100Y – L0201 A INTRODUCTION TO ECONOMICS

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Take-Home Assignment # 2

LAST NAME FIRST NAME STUDENT NUMBER

te: This Take-Home Assignment is due on July 20. The assignment must be hand-itten and all pages must be stapled. Late submissions and submissions by fax/e-

ail will not be accepted. Clearly write your full name and student number.

Question 1: /12 Question 2: /16 Question 3: /10 Question 4: /16 Question 5: /18 Question 6: /18 Question 7: /10

Total : /100

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Question 1 (12 marks) The following table shows several methods of producing 1000 rubber tires per day. There are two factors of production, labour and capital, with prices per unit of $2 and $4, respectively.

Production Method

Units of Labour

Units of Capital

Total Cost (1)

Total Cost (2)

A 140 20

B 90 25

C 70 30

D 35 55

E 25 70

F 20 95 a) Compute the total cost for each production method and fill in the “Total Cost (1)” column in the

table above. (2 marks) Which production method minimizes costs for producing 1000 tires? (1 mark)

b) Plot the isoquant for 1000 tires on the diagram below. (2 marks)

K

80

40

L 40 80 120

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c) Given the factor prices, draw on the same diagram the isocost line that corresponds to the cost-minimizing production method indicating the values of the vertical and horizontal intercepts. (2 marks) What is the equation for this isocost line? (2 marks)

d) Now suppose that the price of capital falls to $2 per unit (while the price of labour continues at

$2 per unit) but the firm still wants to produce 1000 tires per day. Compute the new total cost for each production method and fill in the “Total Cost (2)” column in the table above. (1 mark) Which of the above production methods will the firm adopt now? (1 mark) Explain how a cost-minimizing firm adjusts to this change (with no change in technology). (1 mark)

Question 2 (16 marks) Consider the table below showing the supply schedules for three competitive firms, each producing honey. These three firms make up the entire industry.

Output (kg/day) Market Price ($/kg) Firm A Firm B Firm C Industry 0.50 0 0 0 1.00 25 0 0 1.50 50 0 0 2.00 75 0 0 2.50 100 0 0 3.00 125 50 0 3.50 150 100 0 4.00 175 150 75 4.50 200 200 150 5.00 225 250 225 5.50 250 300 300 6.00 275 350 375

a) Compute the industry’s quantity supplied at each price level and fill in the table. (1 mark)

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b) Plot the supply curve for each firm and for the industry as a whole. Scale each curve as needed. (4 marks)

y$

6.00

4.00

2.00

100 200 100 100 200 200Kg Kg Kg c) Explain why Firm A produces no output at prices $0.50 and lower, why Firm B produ

output at prices $2.50 and lower, and why firm C produces no output at prices $3.50(2 mark)

d) For P ≥ $0.50 the expression for Firm A’s supply curve is P = 0.50 + 0.02 Q – where

price of one kilogram of honey and Q is the quantity of honey in kilograms – and foris Q = 0. Write similar expressions for the supply curves of Firms B and C. (4 marks

Page

Industr
Firm A Firm B Firm C
400 200 Kg

ces no and lower.

P is the P < $0.50 )

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e) Suppose the demand curve for honey is given by the expression P = 6 – 0.005 Q. Fill in the table below with quantity demanded at each price level. (1 mark) What is the market price for honey? What is the quantity transacted in the market? (2 marks) How much will each of the three firms produce? (2 marks)

Price Quantity

Demanded 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00

Question 3 (10 marks) What, if anything, does each one of the following tell you about the ease to entry into or exit from an industry? Briefly explain. a) Profits have been very high for two decades. (2 marks)

b) No new firms have entered the industry for 20 years. (2 marks)

c) The average age of the firms in the 40-year-old industry is less than 7 years. (2 marks)

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d) Most existing firms are using obsolete equipment alongside newer, more modern equipment. (2 marks)

e) Profits are low or negative; many firms are still producing, but from steadily aging equipment. (2 marks)

Question 4 (16 marks) A firm is operating in an industry in which it is technologically possible to construct only two classes of plants. Class A plant is highly automated (i.e., more capital-intensive), requiring an initial fixed-cost investment of $500,000 and having a marginal cost of $2 per unit of output. Class B plant is less automated (i.e., more labour-intensive), requiring an initial investment of $100,000 and having a marginal cost of $4 per unit of output. a) Write the equation of the total cost (TC) for each class of plant. (2 marks)

b) Write the equations of the average total cost (ATC), average fixed cost (AFC), and average

variable cost (AVC) for each class of the plant. (6 marks)

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c) Draw the two ATC curves in the diagram below. (2 marks) 12

Ave

rage

Tot

al C

ost

8

4 200 400 600 800

) d) If this firm were to produce 150,000 u

were to produce 300,000 units of out

e) Over what range of output should thi

should this firm use Class B plant? (2

Output (thousands

nits of output, which plant should it use? (2 marks) If it put, which plant should it use? (2 marks)

s firm use Class A plant? Over what range of output marks)

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Question 5 (18 marks) Consider a price-discriminating Canadian firm that sells its output in two countries (i.e., in two markets): Canada and Argentina. This firm has a constant marginal cost of $30 per unit. The Canadian and Argentinean demand curves are given by the following expressions:

Canadian demand: Q = 150 – P Argentinean demand: Q = 200 – 2 P

where the price (P) is expressed in dollars in both markets, and quantity (Q) is thousand of units per year. P P

100

a 150 50 75

What is the expressa)

b)

Plot the demand cuon the diagrams ab

Canada

150

100

50

Q 50 100 150

ion for the marginal revenue (MR) curve in each

rves (D) and the marginal revenue curves (MR) ove. (2 marks)

Argentin

Q100 150

market? (2 mark)

for Canada and Argentina

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c) If the firm is able to price-discriminate, what is the profit maximizing price and quantity sold in each market? (3 marks) Show these equilibriums in the diagrams above. (1 mark)

d) Compute the price elasticity of demand (at the profit-maximizing points) in each market segment. Does the market segment with less elastic demand have the higher price? (2 marks)

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e) Suppose now that international law forbids this firm to price-discriminate, and thus the firm must charge the same price in both countries (i.e., the firm is now facing a single market). What are the equations for the demand curve (D) and the marginal revenue curve (MR) for this single market. (4 marks)

What will the profit maximizing price be in this single market? (2 marks) How much will the firm sell in each country? (2 marks)

f)

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Question 6 (18 marks) The graph below depicts isoquants for two levels of output that could be produced with different combinations of capital and labour.

12

8 124 200

300

Cap

ital

8

4

16

r a) If the price of one unit of labour were $4 a

many units of capital and labour would thiminimum cost? (Note: Use whole units, noDraw the corresponding isocost line on ththis isocost line? (2 marks)

Labou

nd the price of one unit of capital were also $4, how s firm employ to produce 200 units of output at t fractions of units of labour and capital.) (2 marks)

e diagram above. (1 mark) What is the equation for

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b) If the prices of labour and capital were to remain as in part a) and the firm wanted to produce 300 units of output at minimum cost, how much capital and labour would it now employ? (Note: Use whole units, not fractions of units of labour and capital.) (2 marks) Draw the corresponding isocost line on the diagram above. (1 mark) What is the equation for this isocost line? (2 marks)

c) Given a) and b) above, what (if anything) can be said about returns to scale? (3 marks) d) If the price of labour were to change to one-half its original level, and the firm wanted to

produce 300 units of output at minimum cost, how much capital and labour would it now employ? (Note: Use whole units, not fractions of units of labour and capital.) (2 marks) Draw the corresponding isocost line on the diagram above. (1 mark) What is the equation for this isocost line? (2 marks)

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Question 7 (10 marks) Let Q = 2 L½ K½ be our production function, and let w = $4 and r = $8. The corresponding expressions for the MPL and the MPK are as follows: MPL = (K/L)½ and MPK = (L/K)½. a) State the conditions for cost minimization. (2 marks) b) What combination of labour and capital will a firm select if it wants to produce 1000 units at the

least cost? (3 marks)

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c) What is the total cost of producing 1000 units? (2 marks) d) Suppose the firm’s spending constraint is $10,000. What is the maximum output the firm can

produce? What are the values of K and L? (3 marks)

ECO 100Y – L0201 A INTRODUCTION TO ECONOMICS Take-Home...

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