Px

ED=4 40

25

10

ED=1

ED=1/4

QDX/t

Px

2

1

QDX/t

1/2

2.5 5 10

Review Questions III – Fall 2011 with ANSWERS

1) Suppose the inverse demand for good x is given by the formula Px = 50 – 2*Qx.

Using calculus, solve for the value of the elasticity of demand for x (Edx) in the following

cases.

What is the value of the elasticity of demand when Px = 25?

What is the value of the elasticity of demand when Px = 40?

What is the value of the elasticity of demand when Px = 10?

Are the values you compute for Edx consistent with our

discussion of how the Edx will vary along a linear demand

curve?

Yes

PX = 50 – 2QDX

ED =

= = 1 = = 4 = = ¼

As P along DX, ED

2) Suppose the demand function for good X is given by:

Qdx = 5*(1/P)=5*P-1

. Graph this demand curve for several possible values of P.

Does the elasticity of demand vary along this demand curve the way it does along a linear

demand curve? (If you need help, see the discussion on page 44 of the Browning and Zupan

text.)

QDX = 5P-1

= = = 1

P

Q/t

D

P1

Q1

S2

S1

Q/t

Dx P1

Q1

STAX

S

Q2

3) Suppose the inverse supply function for good x can be described by:

PX = Z + W*Qsx, where Z=10 and W=2

Compute the elasticity of supply: when Q=10, when Q=11, when Q=12…Is the impact of

this change in quantity on the elasticity of supply consistent with the discussion we had in

class concerning the change in elasticity of supply along a supply curve?

Yes

Px = 10 + 2Qs

As Q ES approaching 1

4) Suppose supply of good X is perfectly inelastic. Using the logic (or method) discussed in

class, what would be the impact on supply if a per unit excise tax was imposed on good X?

Tax S1 moves vertically upward

No effect on P1 Q1

5) Suppose goods X & Y are perfect substitutes and both are produced in perfectly competitive

markets. How would the imposition of an excise tax on good X affect the price of good X?

Tax Q, No effect on P

Q/t

Dx $10

50

STAX

S

40

$2

6) How is the government revenue from an excise tax computed? If the demand for a product is

perfectly elastic, does this mean that the government would receive no revenue from

imposing an excise tax on this good?

No.

Suppose tax = $2

After the tax, government revenue

would be $2.40 = $80

Seller pays full burden of the tax.

7) How are the concepts of market “surplus” and market “shortage” relevant to the process of

market adjustment to a new equilibrium after an exogenous shock changes either supply or

demand?

See the discussion in the foundational materials on the class website. After a change in demand

or supply, the resulting surplus or shortage at the initial equilibrium price will create the forces to

move the market to the new equilibrium.

8) In what sense could a drought in the summer of 2011, that substantially reduces the supply of

corn, lead to improved profitability for farmers in 2011?

Quantity offered would decrease. If demand were inelastic, total revenue would increase. If costs

of production were not affected or increased by a sufficiently small amount, profits would

increase.

9) In what sense could one argue that production costs are a special case of opportunity costs?

Expenditures on production have alternative uses.

10) What argument would you give to support the following statement. “A government subsidy

on the purchase of gas efficient hybrid cars would have a greater impact, and government cost, in

the long term than in the short term.”

Demand becomes more elastic in the long term …. Leading to a larger response to the subsidy.

$Px

QDx

D

P1

Q1

ED<1

ED>1

ED=1

$

QDx

Q1

Total Expenditure Function

$ Px

QDx

D

$TE

QDx

Total Expenditure

Function

11) If the elasticity of demand equals 3, what would be the required percentage increase in price

necessary to decrease quantity demanded by 12%?

12) If demand is linear, what is the general shape of the total expenditure function, where we

plot, $ on the Y axis, and quantity demanded on the X axis?

13) If the elasticity of demand is equal to 1 at all price levels, what is the general shape of the

total expenditure function, where we plot, $ on the Y axis, and quantity demanded on the X

axis?

14) What is the equation for the derivative of total spending to a change in price (dPQ/dP)? What

is the interpretation of this equation?

EDx > 1 then 0

EDx = 1 then 0

EDx < 1 then 0

$Px

QSx

S

$

Qx

S1

D

STAX

P+t

P1

t = tax

15) What is the equation for the derivative of total spending to a change in quantity (dPQ/dQ)?

What is the interpretation of this equation?

If EDx > 1 then MR > 0

If EDx = 1 then MR = 0

If EDx < 1 then MR < 0

16) If the inverse supply curve is linear, and has a positive intercept, how does the value of the

elasticity of supply vary along the supply curve? Make up an example of such a supply

curve. Calculate the elasticity of supply as several possible prices. Do the values you

calculate support your answer to the first part of this question?

If P > X, then as P , approaches 1

Suppose P = 5 + QS (inverse supply function)

P = 6 QS = 1

ES = (1/1.5) / (1/6.5) = = 4.33

P = 7 QS = 2

ES = (1/2.5) / (1/6.5) = = 3

P = 8 QS = 3

17) Why do we expect “length of time” to affect both the relative elasticity of demand and

supply?

The longer the period of time, the longer consumers have to “find or adjust” to substitutes.

The longer the period of time, the longer firms have to “adjust” production capabilities.

18) Using the concepts of relative elasticity of demand and supply, address the following

situations graphically.

A) Imposition of a per unit tax on sellers, when demand is perfectly inelastic?

Price increases by the full amount of the tax,

no effect on QE.

QX

S

D

PE

PFLOOR

QE

Short Term

QX

S

D

QE

PE

PFLOOR

Long Term

S

D

PCEILING

QE Q

S

S

D

QE

PCEILING

QS

B) The impact on unemployment, the quantity demanded of workers, and aggregate worker

earnings, of a price floor (minimum wage) in the labor market in the very short term and

the very long term.

Long term: unemployment grows, QD falls by larger amounts, total wages grow less (or

fall more) as ED .

C) The impact on availability of apartments after the imposition of a binding price ceiling, in

the short term and the long term.

QS falls more in long term as S becomes more elastic.