Lecture #1

Review: Market Demand

If you demand something, then you

1. Want it,

2. Can afford it, and

3. Have made a definite plan to buy it.

Wants are the unlimited desires or wishes people have for goods and services. Demand reflects a decision about which wants to satisfy.

Definition: The quantity demanded of a good or service is the amount that consumers plan to buy during a particular time period, at a particular price.

Determinants of Quantity Demanded of a Good (say, good X)

Price of Good X for example, PX then QX (or PX then QX ). The relationship between price and quantity for most goods is negative. Given data on this relationship, we can proceed to map the demand curve for good X.

Review: Market Demand

For the given data PX QX2 6

3 5

4 4

5 3

6 2

4 5 6QX

PX

2

3

4

D

2 3

5

6

Market demand is defined only when all variables other than the price of the good in question (PX) are held constant.

Review: Market Demand

Any change in those other variables serves to change the location of Market Demand (i.e. they cause shifts in the demand curve).

These shift variables could be:

The Price of Other Goods (i.e. good Y) for example,

PY then QX (complementary goods)

PY then QX (substitute goods)

The relationship between the price of Y and quantity of X depends on the relationship between the uses of the two goods.

Changes in Income (M) for example,

If when M then QX (we have an inferior good)

If when M then QX (we have a normal good)

More on this later

Consumer Tastes / Preferences Income Distribution

Credit Availability Government Policies

Future Expectations in the Market and others

Review: Market Demand

The LAW OF DEMAND: states that other things remaining the same, the higher the price of a good, the smaller is the quantity demanded (or the lower the price of a good, the larger is the quantity demanded).

The LAW OF DEMAND results from the combined influences of the substitution effect and the income effect.

Substitution effectwhen the relative price (opportunity cost) of a good or service rises, people seek substitutes for it, so the quantity demanded decreases (not a proper definitionmore later in the course).

Income effectwhen the price of a good or service rises relative to income, people cannot afford all the things they previously bought, so the quantity demanded decreases (not a proper definitionmore later in the course).

Distinction between Market Demand (D) and Quantity Demanded (Q)

P

Q

P

Q

D

Market Demand (D) is a curve representing the complete relationship between price and quantity demanded, normally a downward-sloping curve in price-quantity space.

Quantity demanded (Q) is a distance along the horizontal axis.

Movement Along a Demand Curve

Movement along Demand occurs when only the price of the good in question changes, ceteris paribus*.

In our example, all other variables that affect Q are assumed to remain constant, and thus the position of the demand curve does not change.

* Ceteris paribus is a term used in economics to indicate all other factors held constant.

P P

Q Q

-

+

+

-

-

D D

As P then Q As P then Q

Shifts in the Demand Curve

P

Q

D0

D1

P1

P0

Q1

Assume something occurs to shift the demand curve to the right. For example, income (M) goes up and the good is a normal good.

A shift in Demand occurs when something other than the price of the good in question changes. In this case, as income increases the consumer will respond by increasing the quantity demanded at any price level (when the good is a normal good).

Q1|Q0 Q0

|

Other Examples of Demand Shifts (for example, Wheat)

D

DI

M and wheat is an inferior good.

Pw

Qw

Pw

Qw

DI

D

Pcorn

Corn is a substitute for wheat. As corn becomes more expensive consumers switch to the now cheaper wheat.

Pw

Qw

D

DI

Pmilk - Milk is a complement of wheat. As milk becomes more expensive so does the consumption of wheat with milk. Consumers switch to any now cheaper substitutes of wheat and milk.

Notice that these shifts in demand are not induced by a change in the price of wheat, but by changes in other variables that affect the quantity demanded of wheat.

Math Review: Simple Derivatives

The derivative of a function y = f(x) is defined to be

df(x) = lim f(x + x) f(x)dx x0 x

In words, the derivative is the limit of the rate of change of y with respect to x as the change in x approaches 0. The derivative gives us the most precise meaning to the phrase the rate of change of y with respect to x for small changes in x.

We can denote the derivative of f(x) with respect to x by f|(x).

So, df(x) = dy = f|(x)(all the same, just different notations)dx dx

Lets do a few examples,

The general equation of a line is y = a + bX. Using the general formula for the derivative

df(x) = lim f(x + x) f(x) and subbing in y = f(x)dx x0 x

df(x) = lim a + b(x + x) (a + bx) = b x = bsimply the slope of the line!dx x0 x x

For nonlinear functions, like y = x2 we use the same process. Using the general formula for the derivative

df(x) = lim f(x + x) f(x) and subbing in y = f(x)dx x0 x

df(x) = lim (x + x)2 x2 = x2 +2xx + (x)2 x2 = 2x + x = 2x (as x 0)dx x0 x x

For more complex nonlinear functions, like y = zx2 we use the same process. Using the general formula for the derivative

df(x) = lim f(x + x) f(x) and subbing in y = f(x)dx x0 x

df(x) = lim z(x + x)2 zx2 = zx2 +2zxx + z(x)2 zx2 = 2zx + zx = 2zx (as x 0)dx x0 x x

Some examples will illustrate these general results.

Linear function

Suppose y = 17 3x. Then dy/dx = 3. Generally, if y = a + bx then dy/dx = b.

Nonlinear function

Suppose y = 6x2. Then dy/dx = 12x. Suppose y = 5x3. Then dy/dx = 15x2.Suppose y = 4x4. Then dy/dx = 16x3. Suppose y = 3x5. Then dy/dx = 15x4.Generally, if y = cxn. Then dy/dx = cnxn-1.

Some examples will illustrate these general results.

Multi-variable Nonlinear function

Suppose U = 2x2y2. Then dU/dx = 4xy2.Suppose U = x1/2 y1/2. Then dU/dx = 0.5x-1/2 y1/2 or dU/dx = y1/2

2 x1/2

Generally, if U = cxnym. Then dU/dx = cnxn-1ym.

Price Elasticity of Demand (ed)

Definition:ed = % in qw

% in pw

the percentage change in quantity demanded as a result of a percentage change in the price of the same good.

This is the own price elasticity of demand. Note that when we have downward sloping demand curves this price elasticity is negative since there is an inverse relationship between price and quantity demanded. Normally, we think of ed in terms of absolute value (i.e. we ignore the negative sign when we say it aloudbut it is important to remember that it is always negative whenever we do calculations).

We can write ed as ed = Q/Q = Q . PP/P P Q (called point elasticity)

Note that ed = Q . P Q (slope of the demand curve)P Q P

The elasticity depends on the position of the point where we are evaluating it, as well as, on the slope of the demand curve. The point formula is used to measure elasticity at a particular point on the Demand curve. However, the price elasticity of demand varies along the demand curve.

If you remember, in ECON 101 you were asked to use the arc elasticity formula

ed = Q = Q . (P1 + P2)(Q1 + Q2)/2 P (Q1 + Q2)

P(P1 + P2)/2

This expression is a linear approximation of the demand elasticity and it becomes more and more inaccurate as the distance between Q1 and Q2 becomes larger.

QP

A

B

D

P1

P2

Q1 Q2

What this ARC elasticity formula is really measuring is the midpoint elasticity of a line connecting point A and point B! This is why we prefer the POINT elasticity formulait is accurate.

ed = Q/Q = Q . P measures the elasticity at the point of interest.P/P P Q

The following Demand curves are both special cases where one of the variables (P or Q) are constant.

Perfectly Inelastic Demand

ed = % in Q = 0 = 0% in P % in P

D

P

Q

P

Q

D

Perfectly Elastic Demand

ed = % in Q = % in Q = % in P 0

For demand elasticities in between these two extremes, we know that the main determinant of the degree of price elasticity of demand is the availability of substitutes.

Pcola

Qcola

Pgas

Qgas

D

+

-

D

+

-

Demand Elastic (flatter)

There are many close substitutes for cola.

Demand Inelastic (steeper)

There are very few close substitutes for gasoline.

In terms of numerical values for the price elasticity of demand, we can summarize as follows:

P

QD

Inelastic

0 < ed < 1

few close substitutes

necessities

short run

P

Q

D

Unit Elasticed = 1

P

Q

D

Elastic

1 < ed <

many close substitutes

luxuries

long run

Price Elasticity Along a Straight-Line Demand Curve

Along a straight-line demand curve, ed, is calculated as the ratio of two segments separated by the point of interest.

V

F

H

V

F

H

V

F

H

ed = FH / FV > 1

At F, demand is elastic.

ed = FH / FV = 1

At F, demand is unit elastic.

ed = FH / FV < 1

At F, demand is inelastic.

So, the ranges of ed along a straight-line demand curve are:

P

Q

V

M

H

Recall, the ratio ed = FH / FV

If F is the point V, then ed =

(Demand is perfectly elastic at V)

If F is the point H, then ed = 0

(Demand is perfectly inelastic at H)

If F is the point M, then ed = 1

(Demand is unit elastic at the midpoint of a straight-line demand curve)

If F falls between V and M then ed > 1 and demand is elastic at the point of interest,

F.

If F falls between M and H then ed < 1 and demand is inelastic at the point of

interest, F.

Why is demand more elastic at higher prices than at lower prices?

Q

P

0 2 4 6 8 10 12

2

12

10

8

6

4

V

B

H

A

+2

-2

+2

-2

At a price like P1 = 8, a $2 increase in price (to P1 = 10) results in a 50% drop in quantity demanded. We can see that Q falls from 4 units to 2 units. At such high prices, the consumer finds that more and more substitutes are affordable.

However, at a price like P2 = 2, a $2 increase in price (to P2 = 4) results in only a 20% reduction in quantity demanded. We can see that Q drops from 10 units to 8 units. At lower prices there are fewer affordable substitutes.

What are the 2 price elasticities in this example (i.e. at point A and point B)?

At point A: ed = AH / AV ed = 10 / 2 ed = 5

At point B: ed = BH / BV ed = 4 / 8 ed =

Shifts in Demand and Price Elasticity

A parallel shift in demand to the right (raises / lowers) the price elasticity at any given price level.

P

Q

P1

V

H

V

H

+ +- -

A B

Clearly, AH / AV > BH / BV

This means that on the new demand curve the same price increase causes a smaller (percentage) decrease in the quantity demanded. Said differently, the price elasticity at any given price has fallen.

We should remember that the price elasticity depends upon the slope of the demand curve and ALSO upon P and Q.