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Estimate the demand function

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Reference no: EM131767

Question 1

A firm with market power has estimated the following 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 increase by 50 cents for each unit produced.

a) Write the equation for the firm's total cost function

b) Write the equation for the firm's marginal cost function

c) Write the equation for firm's total revenue function (in terms of Q)

d) Write the equation for the firm's marginal revenue function (in terms of Q)

e) Assume the firm's objective is to maximize profit, and determine

  • The quantity of output it should produce
  • The price it should charge
  • The annual profit it will make

f) Given the price calculated in (e), what is the markup over AVC?

g) Calculate the price elasticity of demand at the price-quantity combination determined in part (e), and use it to determine the profit-maximizing markup. Compare with the markup calculated in (f). Do you find the result of the comparison surprising? Why or why not?

h) Explain whether the firm will make economic profit

  • In the short run
  • In the long run.

When answering the economic profit question, clearly specify your assumptions and illustrate with a diagram.

Question 2

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 price and quantity (recall that the MR curve has the same intercept as the demand curve, but twice the slope).

b) Now assume the monopolist practices first-degree (perfect) price discrimination, i.e. is able 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 the 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 the two pricing strategies results in greater consumer surplus?

e) How does the choice of pricing strategy affect allocative efficiency in the economy?

Reference no: EM131767

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