Microeconomics
Assignment #4
1) A monopolistic firm faces a demand function q = 600 – p. It has a total cost function described by
c(q) = 100q = T where T is a lump sum tax on this firm.
- a) Calculate the output that the monopolist will choose, the price at which it will sell consumer surplus, producer surplus and the deadweight loss. Show this analysis on a diagram.
- b) If the objective of the regulatory authority is to maximize its own revenue, explain how much lump sum tax it will charge
- c) Now let the regulatory authority charge a specific tax of $t per unit of output, i.e. T = $tq. Calculate the profit maximizing price, output, consumer surplus and tax revenue as a function of t. If the objective is to maximize its own revenue, what would t be? If the objective of the regulatory authority is to maximize consumer surplus, what could it do?
2) A perfectly competitive firm sells two goods. The price for the first good is 36$. The price for the second good is 35$. The total cost for a firm is given by the expression:
TC (Q1, Q2) = 3Q12 + 2Q1Q2 + 3Q22 + 7Q2
- Find the maximum profit and optimal values of Q1 and Q2
- If the firm cannot produce in total more than 6 units, then what would be the maximum profit and the optimal values of Q1 and Q2? Find the answer using the Lagrange multiplier. Find the value of the Lagrange multiplier. What economic interpretation has the Lagrange multiplier in this context?
- Find the consumer surplus at P = 2for the following demand function:
P = 8Q-2/3
