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Suppose we have a Monopolist with the following Demand Curve:

QD = 100 - 10P

Using the Demand curve provided above, convert this into an Inverse Demand curve that is, Solving for P.

Develop the equations for both the Total Revenue Curve, TR, and the Marginal Revenue Curve, MR.

If the Monopolist's Marginal Cost, MC is constant at $5.00, find the Profit Maximizing Quantity and Price in this market.

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Chika Ilonah
Chika IlonahLv10
28 Sep 2019

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Related questions

Suppose the demand curve is QD = 500 - p, and the marginal revenuue function is MR = 500 - 2Q. The monopolist has a constant marginal and averge total cost of $50 per unit.

a) Find the monopolist profit-maxmizing output and price.

b) Calculate the monopolist's profit.

c) What is the Lerner Index for this industry?

Suppose there are 100 firms in a perfectly competitive industry. Each firm has a U-shaped, long-run average cost curve that reaches a minimum of $10 at an output level of 8 units. Marginal costs are given by

MC(q)= q+2

and market demand is given by

Q=1000-20P

a. Find the long-run equilibrium in this market and determine the consumer and producer surplus (in this case, the areas of the triangles).

b. Suppose instead there was a single supplier whose marginal cost curve is

MC(Q) =(1/100)Q+2

i) From the above expression for market demand, determine the monopolist's average revenue curve.

ii) From part (i), find the monopolist's total revenue curve.

iii) Differentiate the expression in part (ii) to obtain the monopolist/s marginal revenue curve.

A monopolist sells in two geographically divided markets, the East and the West. Marginal cost is constant at $50 in both markets (marginal cost is also equal to average total cost). The inverse demand curve in each market is as follows:

PE=450-.5QE

PW=700-QW

a) Find the profit-maximizing quantity, price and profit in each market.

b) In which market is demand more elastic?

c) Show what will happen to the monopolist's profit if it is to charge the same price in both markets (That is, profit if the monopolist treats the markets as if they are the same).

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