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Calculating a Monopolist's Consumer and Producer Surplus

1. A monopolist faces demand given by: P=100-4Q and has marginal costs given by: MC=10+2Q
a. Draw the demand, marginal revenue and marginal cost curves. Calculate and show how much this firm will sell and what it will charge.
b. Calculate the producer surplus with monopoly and the consumer surplus with monopoly.
c. How much would be produced if this were a competitive market? What would be the price?
d. Calculate the consumer and producer surplus for a competitive market.

Solution Preview

a)
P = 100 - 4Q
MC = 10 + 2Q

To find MR, first find Total Revenue (TR):
TR = PQ
TR = (100 - 4Q)Q
TR = 100Q - 4Q^2

MR is the derivative of TR:
MR = 100 - 8Q

The attached file shows the three curves.

The monopolist will produce the quantity where MR = MC:
Let MR = MC
100 - 8Q = 10 + 2Q
90 = 10Q
Q = 9

The firm will charge the price given by the demand curve:
P = 100 - 4Q
P = 100 - 4(9)
P = 64

The firm will sell 9 units and will charge $64.

b)
The consumer surplus is the area between the price and the demand curve. Its shape is a triangle. The base of the ...

Solution Summary

Given the equations of the Demand and Marginal Cost curves of a monopolist, this solution shows step-by-step calculations to find the monopolist's output and price. It then shows how to calculate the consumer surplus and producer surplus in the industry. Response includes an Excel attachment.

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