demand and elasticity. reviewing arc elasticity a review problem with arc elasticity

Demand and Elasticity

Price

A

B

Quantity12 16

3

6

h= (12-16)/((12+16)/2))/

(6-3)/((6+3)/2))

= - (4/14)/(3/4.5)

=

(

(

- 0.429

Reviewing arc elasticity

Price

A

B

Quantity110 16

7

18

h=

0

?

A review problem with arc elasticity.

Point Elasticity

= (dQ/dP) x (P/Q)

Review Perfectly inelastic demand, Perfectly elastic demand.

Unitary price elasticity

Price elasticity and total revenue and marginal revenue

Price elasticity changes along a curve.

Empirical price elasticities.

Price elasticities by degree of luxury on an airline.

Supply curve

D1

D2

D3

P

QSuppose that three different experts working for the Deptof Health estimated the demandfor cigarettes differently. Rate thedemand curves from perfectlyinelastic to the most elastic.

Elasticity is important for cigarette policy.

Supply curve

D1

D2

D3

P

Q

T

T

Then suppose that cigarettesare taxed by T dollars per pack.

Sup p ly c urve

D 1

D 2

D 3

P

QSup p o se tha t thre e d iffe re nt e xp e rts wo rking fo r the De p to f He a lth estim a ted the d e m a ndfo r c ig a re tte s d iffe re ntly. Ra te thed em a nd c urve s fro m p erfe c tlyine la stic to the m ost e la stic .

So, how elastic is the demand of cigarette buyers?

The news item states the Surgeon General’s report that this demand elasticity in absolute value is between 0.3 and 0.5.

Increasing the Michigan price of cigarettes approximately $3.50 to $4.25 is a nearly 25% increase.

To calculate the implied reduction in MI smoking, multiple the 25% times the elasticity estimate (0.3 to 0.5).

That is, a 7.5% to a 12.5% reduction.

On the tax revenue side:

Tax revenue is quantity change times tax change.

So, the change in tax revenue is likely to be:

A (1.00-.075) x Q x $0.75 to (1.00-.125) x Q x $0.75 increase.

Granholm’s administration estimates that this will amount to a $30,000,000 gain in tax revenue for the state, and 150,000 fewer smokers in Michigan. Because the cigarette elasticity for teenagers is larger, Granholm estimates that 94,000 (fewer?) teens will take up smoking in the state. Freep 2/10/04

A useful formula involving price elasticity states that

MR = P(1 + 1/)

Proven this way: We know that d(PQ)/dQ = (dP/dQ)Q + P MR

So, MR = (P/P)[(dP/dQ)Q + P] =

P[dP/dQ)Q/P + 1] = P(1 + 1/)

Income elasticity:

nY = (dQ/dY) x (Y/Q)

Income elasticity empirically.

Cross Price Elasticity

XY = (dQx/dPy)x(Py/Qx)

Price

Quantity

Sup

Dem

Min WageA B

C D

The Minimum Wage Problem

Pric e

Q ua ntity

Sup

Dem

M in Wa g eB

C D

The M inim um Wa g e Prob lem

Le ss e la stic la b o rd e m a nd m e a nsle ss d e c line in e m p lo ym e nt

P

Q

De m A

De m B Sup p A

Sup p B

Whe the r fa rm e rs b e ne fit fro m a b um p e rc ro p d e p e nd s o n the e la stic ity o f d e m a nd

Pric e

Q ua ntity

Dem a nd (ine la stic c a se)

2.50

120

110

5.50

Revenue effect when demand is inelastic.

Q ua ntity

Pric e

De m a nd

Pe rfe c tly e la stic d e m a nd

Q ua ntity

Pric e

De m a nd

Pe rfe c tly ine la stic d e m a nd