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Three (3) identical firms produce widgets. Each firm faces a constant marginal cost of $10 per widget, and has fixed costs of $15,000. The firms compete by selecting quantities (Cournot Competition). Inverse demand in the market is given by the equation, P = 50 - Q 100, where P represents the market price and Q is the total quantity produced by the three firms.
(a) Derive the total cost function for the typical firm. (Hint: Use QA to represent the quantity produced by this firm.)
(b) Derive the profit function for the typical firm. (Hint: Use X to represent the combined production of the remaining two firms.)
(c) Derive the best response function for the typical firm.
(d) Find the equilibrium quantity of the typical firm.
(e) Find the equilibrium market price and the profits of the typical firm.
(f) Explain how would you expect the structure of this market to change over time.
What does it mean that a firm is pricing its product based on "whatever the market will bear"? Why is the concept of equilibrium (such as a market equilibrium) important when understanding a social science?
Estimate the linear model described in part (a) using Ordinary Least Squares regression and display your regression results.
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