Answer to Question #23035 in Microeconomics for James

Question

1. Consider a competitive firm. Its marginal cost function is MC(q)=2q and the market price is $20.
How much output will this firm produce?
2. Consider a competitive firm. Its cost function is c(q)=2q
2
and the market price is $20. How much
output will this firm produce?
3. Consider a competitive firm. Its cost function is c(q)=2q and the market price is $10. Write down the
revenue and the marginal revenue function.

5. Why does a tax create a deadweight loss? What determines the size of this loss?

Answer 1

1. Consider a competitive firm. Its marginal cost function is MC(q)=2q and the market price is $20. How much output will this firm produce?
MR = MC = P,
MC = 2q = 20,
q = 10

2. Consider a competitive firm. Its cost function is c(q)=2q2 and the market price is $20. How much output will this firm produce?
MC = c'(q) = (2q2)' = 4q,
4q = 20,
q = 5

3. Consider a competitive firm. Its cost function is c(q)=2q and the market price is $10. Write down the revenue and the marginal revenue function.
TR = P*q = 10q, MR = TR' = 10

5. Why does a tax create a deadweight loss? What determines the size of this loss?
A tax creates deadweight loss by artificially increasing price above the free market level, thus reducing the equilibrium quantity. This reduction in demand reduces consumer as well as producer surplus. The size of the deadweight loss depends on the elasticities of supply and demand. As the elasticity of demand increases and the elasticity of supply decreases, i.e., as supply becomes more inelastic, the deadweight loss becomes larger.