Question

In: Economics

1. Suppose the Demand curve for heaters is P = 100 – Q. Suppose firms face...

1. Suppose the Demand curve for heaters is P = 100 – Q. Suppose firms face a constant Marginal Cost of $20 per heater. In perfect competition (part 2 of the class) we learned that the competitive price of heaters would be $20 (with constant MC, MC = AC). What would the monopoly price and quantity of heaters be? Compare the welfare of these two markets (consumer surplus, producer surplus, and deadweight loss).  (2 pts)

Solutions

Expert Solution

A monopolist produces the profit maximising level of output at a point where the marginal revenue equals the marginal cost.

TR = P * Q

TR = (100 - Q) * Q

TR = 100Q - Q2

MR = change in TR/change in Q.

MR = 100 - 2Q.

MC = $20,

MR = MC,

100 - 2Q = 20

80 = 2Q

Q = 40 units.

P = 100 - 40 = $60.

Under perfect competition, P = MC,

100 - Q = 20

Q = 80 units.

P = 100 - 80

P = $20.

Under monopoly, orange shaded is the consumer surplus, lying above the price line and below the demand curve.

Green shaded is the producer surplus, lying below the price line and above the cost curve.

Grey shaded is the deadweight loss.

Under perfect competition, there is no deadweight loss and producer surplus because the working is efficient and resources are optimally allocated.

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

CS = 1/2 * (40 - 0) * (100 - 60).

CS = $800.

PS = 1/2 * (60 - 20) * (40 - 0)

PS = $800.

DWL = 1/2 * (60 - 20) * (80 - 40)

DWL = $800.

CS under competition is the area ABC.

CS = 1/2 * (100 - 20) * (80 - 0)

CS = $3200.

Therefore, the CS is higher in case on perfectg competition as the price charged is equal to the marginal cost. and there is no economic profit earned.


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