Question

Consider a perfectly competitive market for a good with the following supply and demand curves:

Qd= 400–P and Qs= 80 + 4P

a. Calculate the change in equilibrium quantity, and the size of the deadweight loss that will result if a unit tax of $10 is imposedon consumers of this good. Draw a graph that illustrates how you arrived at your answer.

b. Suppose the demand curve changes to:

Qd’= 376-0.6P First, verify that the pre-tax equilibrium is approximately the same with this new demand

curve. By how much does quantity change when a $10 tax is imposed on consumers? Based

on this answer, what should happen to the deadweight loss (relative to part a)? Calculate the

value of deadweight loss with the new demand curve to verify your intuition about the answer to the previous question. You can round your answers to the tenths place.

Answer 1

Qd = 400-P i.e. P = 400-Qd

Qs = 80+4P i.e. P = Qs/4 -20

To calculate equilibrium price P0 and quantity Q0 at this level, lets equate to equations (Demand = supply)

400-P = 80+4P

5P = 320

P0 = 64

At P0 of $64, Q0 will come out to be 336 units

a) If tax of $10 is imposed by government then,

P+10 = 400-Q as now consumers have to pay $10 extra to purchase a unit

P = 390-Q

New equilibrium qty and price will be calculated by equating dd equation with ss equation

390-Q = Q/4 - 20

Q1 (New quilibrium quantity) = 328

P1 (New equlibrium price) post tax = 400-Q1 = 400-328 = 72

Resulting dead weight loss will be = 0.5*(Q1-Q0)*(P1-P0) = 0.5*8*8 = 32 (area of red triangle refer to attached image).

Date / Page No. p. S 328 -336

(b) New Qd' = 376-0.6P

New Equilibrium qty and price will be

376-0.6P = 80+4P

P0' = 64.3 = 64

Q0' = 376-0.6*64.3 = 337.4 = 337

If $10 tax is imposed then dd equation will be

0.6P + 10 = 376-Q

P = 617 - Q/0.6

New Equilibrium qty and price by equating new dd equation withh ss will come out to be 332 units and $ 73 respectively.

New Dead weight loss = 0.5*(337-332)*(73-64) = $22.5

Resulting dead weight loss has decreased because as per new dd curve consumers have now become less inelastic and thus producers will have to share a burd