problem1
A firm with market power has estimated the subsequent demand function for its product:
Q = 12,000 – 4,000 P
Where P = price per unit and Q = quantity demanded per year.
The firm’s total costs are $4,000 when nothing is being produced. These costs raise by 50 cents for each unit produced.
a) prepare an equation for the firm’s total cost function
b) prepare an equation for the firm’s marginal cost function
c) prepare an equation for firm’s total revenue function (in terms of Q)
d) prepare an equation for the firm’s marginal revenue function (in terms of Q)
e) Assume the firm’s goal is to maximize profit, and determine
• The quantity of output it should produce
• The price it must charge
• The annual profit it will make
f) Given the price find outd in (e), what is the markup over AVC?
g) Compute the price elasticity of demand at the price-quantity combination determined in part (e), and uses it to determine the profit-maximizing markup. Compare with the markup find outd in (f). Do you find the result of the comparison surprising? Why or why not?
h) Elucidate whether the firm will make economic profit
• In the short run
• In the long run.
When answering the economic profit problem, clearly specify your assumptions and demonstrate with a diagram.
problem2
A monopoly firm faces a demand curve P = 120 – Q. The monopolist’s marginal cost curve (MC) is constant at MC = $4.
a) Determine the non-discriminating monopolist’s profit-maximizing quantity and price
(Recall that the MR curves has the same intercept as the demand curve, but twice slopes).
b) Now suppose the monopolist practices first-degree (perfect) price discrimination, that is, is capable to charge a different price to each customer. What is the quantity sold under this policy? What is the price charged for the last unit just sold?
c) Which of two pricing strategies (single price vs. perfect price discrimination) results in greater social welfare (measured by the sum of the consumer and producer surplus)?
d) Which of two pricing strategies results in greater consumer surplus?
e) How does the choice of pricing strategy affect allocate efficiency in economy?