Economics 202: Intermediate Microeconomic Theory

1. Please turn in Review #1

2. Please read Chapter 7 (most of it will be for Tue)

Demand Elasticity• We assume all D-curves have a downward-slope, but how steep

one is depends on the commodity.

• A reduction in the Pmilk may lead to a small increase in purchases, but a in Pairline may lead to a big increase in purchases.

• Own-Price Elasticity of Demand = X,Px = % QdX / % PX

– Just how sensitive is qty demanded to a change in price? = (Q/Q)/(P/P) = (Q/P)*(P/Q) = (1/slope)*(P/Q)

• = (Q/ P)*(P/Q)

• If < -1 we say D for that good is elastic> -1 D is inelastic = -1 D is unit-elastic

Demand Elasticity• Find the elasticity of a D-curve: Q = a - bP.

• Properties of Price Elasticity of Demand when D-curve is linear

– it is different at every point along the D-curveapproaching - at vertical intercept, 0 at

horizontal intercept

– it is never positive (always negative, except one point)

– it is inversely related to the slope of the linear D-curve

• Two polar cases

– slope of D-curve is much easier to calculate, so why bother with elasticity at all?

More Demand Elasticities• Income elasticity of demand measures how responsive consumption of a good is to a change

in income

X,I |Px,Py= (QdX/Qd

X)/( I/I)

If X,I > 0, then the good is normal.

Luxury good, X,I > 1 (eat out = 1.4; dentist = 1.42)

Necessity, 1 > X,I > 0 (food bought for home = 0.5; physician = 0.75)

If X,I < 0, then the good is inferior.

• Cross-price elasticity of demand measures how responsive consumption of good X is to a change in price of good Y.

X,Py |Px,I = ( QdX/Qd

X)/( PY/PY)

If X,Py > 0, then X and Y are substitutes.

If X,Py < 0, then X and Y are complements.

Often used in anti-trust cases to measure how competitive a market may be. Are there substitutes?

Point vs. Arc Elasticity

• Point Elasticity is what we just did

= ( Q/Q)/( P/P) = (Q/ P)*(P/Q)

• Arc elasticity is the same thing except we use the average of the two prices and quantities (“mid-point method”)

arc = ( Q/Qavg)/( P/Pavg) = ( Q/ P)*(Pavg/Qavg)

• for point elasticity, when the changes are small, it doesn’t make a big difference for our result which point we choose

• for arc elasticity, it would make a big difference if we chose 1 point, so we take the average

Elasticity

• Suppose that instead of a linear D-curve, Q = a – bP,

we have Q = 1,200/P as the demand for zip drives.

• This is a hyperbola. PQ = 1,200 regardless of the price.

• Total Expenditure is constant!

• In general, if demand takes the form Q = aPb (b < 0), the price elasticity of demand is constant and equal to b.

• No need to worry about specifying the point at which elasticity is measured.

Elasticity and Total Revenue• GGB toll = $1, then 100,000 trips.

If = -2, what happens to # trips when you toll by 10%? Total revenue?

• When D is: Price and Total expenditure move in:

elastic opposite directions

inelastic the same direction

unit-elastic TE doesn’t change as P changes

D elastic

D inelastic

P

Q

D unit-elastic

Estimates of some ElasticitiesGood or service Own-Price Elasticity of Demand

Green peas -2.8

Cars -1.5

Electricity -1.2

Beer -1.19

Movies -0.87

Foreign Air Travel -0.77

Shoes -0.70

Doctor’s services -0.60

Water -0.40

Theater, opera -0.18

• Determinants of Elasticity of Demand

Using Elasticity• Doctors, through the AMA, restrict the supply of physicians. How does

this affect the incomes of doctors as a group?

• A labor union negotiates a higher wage. How does this affect the incomes of affected workers as a group?

• UNC decides to raise the price of football tickets. How is income from the sale of tickets affected?

• Airlines propose to raise fares by 10%. Will the boost increase revenues?

• Davidson is considering raising tuition by 7%. Will the increase in tuition raise revenues of the college?

• CATS is considering lowering bus fares. Will this decrease CATS’ total receipts?

Probability• The probability of a repetitive event happening is the relative

frequency with which it will occur– probability of obtaining a head on the fair-flip of a coin is 0.5

• If a lottery offers n distinct prizes and the probabilities of winning the prizes are i (i=1,n) then

∑=

=n

ii

1

1π

Expected Value

• For a lottery (X) with prizes x1,x2,…,xn and the probabilities of winning 1,2,…n, the expected value of the lottery is

∑=

=n

iiixXE

1

)(

nnxxxXE +++= ...)( 2211

• The expected value is a weighted sum of the outcomes – the weights are the respective probabilities