Econ 461 - Industrial Organization
Stafford, Spring 2001
Problem Set 3
  1. Assume that firm M (the manufacturer) sells an input to firm R. Now R sells the product to the public, incurring a cost of $6 per lawnmower for its retail services. Let X represent the consumer demand for lawnmowers. Then X = 100 - PR where PR is the retail price of lawnmowers. Assume that both M and R are monopolists.
    1. Find the derived demand for lawnmowers facing M, that is, the retailer's demand for lawnmowers given the price PM set by the manufacturer. To do this, find the MR = MC condition for R, where MC = $6 + PM. Solving for X will give you the derived demand.
    2. If M's total cost function is 10 + 4X + X2, find the equilibrium prices and quantity (i.e., X*, PM*, and PR*) and the profits of the two firms. (You will need to differentiate total costs w.r.t. X to get M's marginal costs.
    3. Assume M and R merge to form a single vertically integrated firm. Find the equilibrium values of PR and x and the profit of the merged firm.
    4. Compare the unintegrated case with the integrated case. Is it true that both the firms and the public would prefer integration?

      5.  
  2. Two firms are engaged in Bertrand competition. There are 10,000 consumers in the market, each of whom is willing to pay up to 10 for one unit of the product. Both firms have a constant marginal cost of 5. Initially each firm is allocated half of the market. It costs a customer s to switch from one firm to the other. All prices are known by customers. Additionally, prices must be in dollar increments (e.g., you can't charge $6.50).
    1. Suppose that s=0.99. What is/are the Nash Equilibrium/Equilibria of this model?
    2. Suppose that s=2.01. What is/are the Nash Equilibrium/Equilibria of this model?
    3. What is value of raising consumer's switching costs from $0.99 to $2.01?

      4.  
  3. You are the CEO of UGLY, Inc. the sole producer of facial oil skin-life extender. You need to determine the advertising budget for next year. The marketing department has provided you with three important items of information: (a) The company is expected to sell $10 million worth of the product; (b) it is estimated that a 1% increase in the advertising budget would increase quantity sold by 0.05%; (c) it is estimated that a 1% increase in the product's price would reduce quantity sold by 0.2%.
    1. How much money would you allocate for advertising next year if you believed in the Dorfman-Steiner rule?
    2. Suppose the marketing department has revised its estimation regarding the demand price elasticity to a 1% increase in price resulting in a reduction of quantity sold of 0.5%. How much money would you allocate to advertising after getting the revised estimate?
From the book:
Exercise 13.7