Question

Answer the questions below using the following equations for supply and demand where Q is the number of computers and P is the price per computer.

QD (P) = 60 - 2P

C(Q) = 15Q

a. Suppose the government determines that a fee of $2 per computer will be implemented to cover pollution externalities in production. What will be the price and quantity under perfect competition? Under monopoly?

b. Do consumers LOSE more surplus from the $2 fee under monopoly or under perfect competition? Calculate the differences under perfect competition and monopoly and compare.

Answer 1

From demand: P = (60 - Q)/2 = 30 - 0.5Q

MC = dC(Q)/dQ = 15

The pollution fee increases MC by $2, so new MC = 15 + 2 = 17

(a)

(i) Perfect competition

Setting P = new MC,

30 - 0.5Q = 17

0.5Q = 13

Q = 26

(ii)

In monopoly, MR = MC.

TR = P x Q = 30Q - 0.5Q2

MR = dTR/dQ = 30 - Q

30 - Q = 17

Q = 13

P = 30 - 0.5 x 13 = 30 - 6.5 = 23.5

(b)

When QD = 0, P = 30

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

(i) Perfect competition

Before tax,

30 - 0.5Q = 15

0.5Q = 15

Q = 30

P = MC = 15

CS before tax = (1/2) x (30 - 15) x 30 = 15 x 15 = 225

CS after tax = (1/2) x (30 - 17) x 26 = 13 x 13 = 169

Loss in CS = 225 - 169 = 56

(ii) Monopoly

Before tax,

30 - Q = 15

Q = 15

P = 30 - 0.5 x 15 = 30 - 7.5 = 22.5

CS before tax = (1/2) x (30 - 22.5) x 15 = 7.5 x 7.5 = 56.25

CS after tax = (1/2) x (30 - 23.5) x 13 = 6.5 x 6.5 = 42.25

Loss in CS = 56.25 - 42.25 = 14

(iii) Therefore, Loss in CS is higher in perfect competition by (56 - 14) = 42.