Question

Using the following information solve for the monopolist output and price, the perfectly competitive output and price, the profits earned under both models and the deadweight loss that arises as a result of the monopoly:

a. Demand: P=500-2Q ; Supply: P=50+3Q; MR=500-4Q

b. Demand: P=1000-5Q ; Supply: P=100+5Q ; MR=1000-10Q

c. Demand: P=400-4Q; Supply: P=40+2Q; MR=400-8Q

Please use calculation instead of graph to find solution.

This is a market demand curve.

Answer 1

a. For monopolist output, MR = MC. Here the info on MC is missing.

Solving this , 500 - 4Q = c where c is the marginal cos, we will get an optimum Q which is the equilibrium quantity. Substitue the optimum value of Q in the market demand function i.e. 500 - 2(Q)and we will get the equilibrium price.

For calculating equilibrium in competitive markets, price is equal to marginal cost. And equilibrium quantity could be calculated by substituting the value of equilibrium price in either demand or supply function.

The same would be done for other parts. Please provide the value of MC in the comments section if it is not clear, i will show you the algebra