Question

A. Assume the market supply and market demand equations for TVs are as follows.

P=420+0.1Qs

P= 1220-2.4Qd

The equilibrium price is $452 and the equilibrium quantity is 320. The technological

advancements allow firms to sell an additional 1,250 units at every price level. Solve for

the new supply curve, new equilibrium price, and new equilibrium quantity.

B. Solve for the change in consumer surplus and for the change in producer surplus from the

technological advancement in part B.

Answer 1

In pre-tax equilibrium, demand equals supply:

420 + 0.1Q = 1220 - 2.4Q

2.5Q = 800

Q = 320

P = 420 + 0.1 x 320 = 420 + 32 = 452

(A) Quantity supplied will increase by 1,250 units at every price, and new supply function becomes

P = 420 + 0.1(Q - 1,250) = 420 + 0.1Q - 125 = 295 + 0.1Q

Equating with demand,

1220 - 2.4Q = 295 + 0.1Q

2.5Q = 925

Q = 370

P = 1220 - (2.4 x 370) = 1220 - 888 = 332

(B)

From demand function, when Qd = 0, P = 1220 (vertical intercept).

Consumer surplus (CS) = Area between demand curve and price

CS before increase in supply = (1/2) x (1220 - 452) x 320 = 160 x 768 = 122,880

CS after increase in supply = (1/2) x (1220 - 332) x 370 = 185 x 888 = 164,280

Increase in CS = 164,280 - 122,880 = 41,400

From original supply function, when Qs = 0, P = 420 (vertical intercept).

Producer surplus (PS) = Area between supply curve and price

PS before increase in supply = (1/2) x (452 - 420) x 320 = 160 x 32 = 5,120

From new supply function, when Qs = 0, P = 295 (vertical intercept).

PS after increase in supply = (1/2) x (332 - 295) x 370 = 185 x 37 = 6,845

Increase in CS = 6,845 - 5,120 = 1,725