Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Chapter 15, Problem 15.5P
b)
To determine
Output and profit of each firm is to be determined.
c)
To determine
Graphical representation of Nash equilibrium and isoprofit is to be determined.
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Consider the following static game with two firms as the players. Each firm must decide either to upgrade (U) an existing good to a new version; or not upgrade it (N). The decisions are simultaneous. If a firm chooses to upgrade, they have to pay a fixed cost of 7. If they don’t upgrade, there is no fixed cost. The marginal cost is always equal to 3. The demand side of the market is as follows: If neither firm upgrades, each firm sells 2 units at price 4. If both firms upgrade, each firm sells 3 units at price 5. If only one firm upgrades, the one who upgrades sells 5 units at price 5, and the other firm does not sell anything.
Two identical firms each have a cost function TC = 2y2 and the market demand for their output is P = -4Q+192a) Write the “best response†function for each firm.b) Find the Nash equilibrium in this model c) Show that if each firm produces 1 fewer units than the result in (b), both firms make more profit. Use this information to construct a normal form game. Explain why this game is a prisoner’s dilemma.
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