Part 1 Limit Pricing


Suppose that market demand is described by P = 100 − (Q + q), where P is the market price, Q is the output of the incumbent firm, and q is the output of a potential entrant to the market. The incumbent firm’s total cost function is T C(Q) = 40Q, whereas the cost function of the entrant is C(q) = 100 + 40q, where 100 is a sunk cost incurred to enter the market.


  1. If the entrant observes the incumbent producing Q0 units of output and expects this output level to be maintained, write down the equation for the residual demand curve that the entrant firm faces.
  2. If the entrant firm maximizes profit given the residual demand curve in (a) what output qe will the entrant produce? (Your answer should be a function of Q0.)
  3. How much output would the incumbent firm have to produce to just keep the entrant out of the market? That is, solve for the limit output Q. At what price will the incumbent sell the limit output?































Part 2 – Network Issue

  1. A) Show that in the network setting, the customers need to achieve a certain critical point in order to make network work.


  1. B) Assume that consumers contemplating buying a network service have reservation prices uniformly distributed on the interval [0, 50] (measured in dollars). Demand by a consumer with reservation price wi for this service is


  1. Calculate the demand function for this service.
  2. What is the critical mas if price is set at $5?
  3. What is the profit-maximizing price for the service?



































Part 3 – Two-sided Market and New Economy


  • In United States Microsoft Corp., Microsoft expert witness Richard Schmalensee testified:

The software industry is intensely competitive. Microsoft does not have monopoly power over operating systems, nor does it act like a company with monopoly power. Microsoft’s pricing for Windows is far, far lower than what a rational, profit- maximizing company with a monopoly over operating systems would charge. Computer manufacturers pay Microsoft a royalty for their license to Windows that is considerably less than 5 percent of the price of a typical new PC. Application of a standard economic formula for pricing by a monopolist shows that Microsoft charges less than one-sixteenth the price for Windows that a monopolist would charge.

  1. Professor Schmalensee is referring to the static monopoly price as defined in figure 3.2 and equation 8.1. How might you come up with an estimate of the static monopoly price?
  2. Assuming it was a monopolist, why might Microsoft price below the static monopoly price?
  3. Do you agree or disagree with Professor Schmalensee? Substantiate your position.


Figure 3.2 (Monopoly versus Competition)





Consider a two-sided platform that matches men and women who are interested in finding a marriage partner. The platform sets a price for men to access the platform and a price for women to access the platform. These prices are chosen to maximize the platform’s profits. Assume the platform is the only one in the market.

  1. What determines which gender pays a higher price?
  2. Suppose a massive immigration wave occurs that increases the fraction of young men in the population relative to young women. How will this affect the male and female prices on the platform?
  3. Suppose the value of marrying exogenously increased for men, while the value of marrying for women was unchanged. Hence, in terms of figure 9.9, the benefit curve rises for men and is unchanged for women. What will happen to the price for men to access the platform? What about the price for women to access the platform?
  4. Now suppose a second platform enters the market. Legislation is passed that allows a man to belong to both platforms but permits a woman to belong to at most one platform. Will this legislation tend to cause the access price for women to be higher or lower than the access price for men?



Figure 9.9: a) Buyer’s value from the platform; b) Seller’s value from the platform



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