Question

Suppose the market demand function is Q = 120 – 2P, and the marginal cost (in dollars) of producing the product is MC = Q, where P is the price of the product and Q is the quantity demanded and/or supplied.

1. How much would be supplied by a competitive market? (Hint: In a perfect competition, the profit maximization condition is MR=P=MC)

2. Compute the consumer surplus and producer surplus. Show that the economic surplus is maximized.

Answer 1

Demand function;

Q = 120 - 2P
2P = 120 - Q
P = 60 - Q/2

where P is the price of the product
Q is the quantity demanded and/or supplied.

Marginal cost;

MC = Q

a) The equilibrium condition is;

P = MR = MC

60 - Q/2 = Q
60 = Q + Q/2
60 = (2Q+Q)/2
120 = 3Q
Q = 40

Therefore, quantity supplied by a competitive market will be; Q = 40

b) The supply curve in a competitive market will be the marginal cost in short run;

P = MC
P = Q

The consumer surplus will be;

CS = 1/2 * 40 * (60-40)
= 20 * 20
CS = 400

The producer surplus will be;

PS = 1/2 * 40 * 40
= 20 * 40
PS = 800

Total economic surplus;

TES = CS + PS
= 400 + 800
TES = 1200

Economic surplus is maximised when marginal benefit from consuming a good is equal to its marginal cost of producing;

P = MC

which is at the point where;

Q = 40

MC = 40

P = 60 - Q/2
= 60 - 40/2
= 60 - 20
P = 40 = MC