Question

In a hypothetical market,
The demand equation is given as: P = 62 - 2Q
The supply equation is given as: P = 13 + 3Q.

Assuming a monopoly market with Q = 7:

1) What is the monopoly market price?
2) What is the consumer surplus?
3) What is producer surplus?
4) What is the total wealth?

Answer 1

Monopolist produces profit maximsing level of output at a point where the marginal revenue equals the marginal cost. The supply curve is nothing but the upward sloping marginal cost curve.

TR = P * Q

TR = (62 - 2Q) * Q

TR = 62Q - 2Q²

MR = TR/Q

MR = 62 - 4Q

MC = 13 + 3Q

62 - 4Q = 13 + 3Q

62 - 13 = 3Q + 4Q

49 = 7Q

Q = 49/7

Q = 7 units.

a. P = 62 - 2*7

P = $48

b. Consumer surplus is the area bounded by above the price line and below the demand curve, this is shaded by orange.

Area of triangle = 1/2 * base * height.

CS = 1/2 * (7-0) * (62 - 48) = $49.

c. Producer surplus is the area bounded by below the price line and above the supply curve (MC curve), this is shaded in green colour.

PS = area of rectangle 48-34-B - A + area of triangle 34-B-13 + area of triangle ABC.

Area of rectangle = Lenght * breadth.

PS = (7-0)*(48-34) + 1/2 * (34-13) * (7-0) + 1/2 * (9.8-7)*(48-34)

PS = 98 + 73.5 + 19.6

PS = $191.1

d. Total wealth = producer surplus + consumer surplus

Total wealth = 191.1 + 49

Total wealth = $240.1