Economics 105 Berger

Homework #2-Answers

1. The following problem deals with the economic effects of imposing a specific tax.

Table 1

P Q^D Q^S(no tax) Q^S(tax)

$15 0 240

14 40 220

13 80 200

12 120 180

11 160 160

10 200 140

9 240 120

8 280 100

7 320 80

a. Draw a supply-demand graph for Table 1 and label the equilibrium price and quantity with numbers.

b. Calculate the producers' surplus (PS) and the consumers' surplus (CS).

CS = 1/2($15-$11)(160) = $320

PS = 1/2($11-$3)(160) = $640

c. Suppose that a specific tax of $3 per unit is levied on producers. After the market completely adjusts to the tax, do the following:

(1) Fill in the numbers for the new supply curve Q^S(tax) and draw the new supply curve on your graph for 1.a. Identify the new equilibrium price and quantity.

Table 1

P Q^D Q^S(no tax) Q^S(tax)

$15 0 240 180

14 40 220 160

13 80 200 140

12 120 180 120

11 160 160 100

10 200 140 80

9 240 120 60

8 280 100 40

7 320 80 20

How were the numbers in the last column in Problem 1.c.(1) computed? Note that each quantity supplied is $3 higher for Q^s-tax. For example, the quantity supplied of 100 is $4 for the no-tax case but $7 for the tax case. Etc.

(2) Calculate the welfare loss (WL) caused by the tax and indicate the area associated with the welfare loss on the graph.

WL = ½($12-$9)(160 - 120) = $60

Notice that the welfare loss can be described as the following: (a) the area under the demand curve between 120 and 160 which represents the value of the goods that consumers lose because their consumption has been reduced from 160 to 120 by the tax (a negative number) plus (b) the area under the supply curve between 120 and 160 which represents the value of the output gained by other sectors (i.e. resources move to their next best alternative use and hence represent a gain to other sectors) equals (c) the welfare loss triangle (a net loss).

(3) Calculate the PS and CS and compare to 1.b.

CS’(tax) = ½($15-$12)(120) = $180

PS’(tax) = ½($9-$3)(120) = $360

NOTE: For the Consumers Surplus (CS) and Producers Surplus (PS) in this part, the price that consumers pay will be the after tax equilibrium price of supply and demand. The price that producers receive will be the price that consumers pay minus the tax (which yields a price on the no-tax supply curve at 120 units).

(4) Calculate the amount of tax revenue collected.

TAX REV = ($3)(120) = $360

NOTE: The sum CS’(tax) + PS’(tax) + TAX REV + WL

= $180 + $360 + $360 + $60 = $960 = CS + PS (before the tax)

2. Using the numbers from the previous example (the no-tax supply), assume a price ceiling is imposed at $7.

a. Draw a graph of this situation and label with the appropriate numbers, indicating the amount of the excess demand (ED).

b. Calculate the size of the PS and CS when the price ceiling is in effect.

CS’(ceiling) = ½($15-$13)(80) + ($13-$7)(80) = $560

PS’(ceiling) = ½(($7-$3)(80) = $160

c. Calculate the welfare loss (aka the deadweight loss) and indicate the area on the graph corresponding to this welfare loss.

Two ways: 1. WL = ½($13-$7)(160-80) = $240

2. CS + PS = $960

CS’(ceiling) + PS’(ceiling) = $720

$960 - $720 = $240