Two neighboring homeowners, 1 and 2, simultaneously choose how many hours to spend maintaining a beautiful lawn (denoted by l 1 and l 2 ). Since the appearance of one’s property depends in part on the beauty of the surrounding neighborhood, homeowner’s benefit is increasing in the hours that neighbor spends on his own lawn. Suppose that 1’s payoff is expressed by
2 units of the firm 1’s good and A − p 2 + p 1
2 units of the firm 2’s good. Assume that the firms have identical (and constant) marginal costs c(< A), and the payoff for each firm is equal to the firm’s profit, denoted by π 1 and π 2 .
Q = K 1 =4
L 1 =8 Then, answer the following questions.
(a) In the short run, the …rm is committed to hire a …xed amount of capital K(+1), and can vary its output Q only by employing an appropriate amount of labor L . Derive the …rm’s short-run total, average, and marginal cost functions. (b) In the long run, the …rm can vary both capital and labor. Derive the …rm’s
(b) If consumer’s choice satis…es the weak axiom of revealed preferences, we can always construct a utility function which is consistent with such choice behav- iour.
(c) If a consumer problem has a solution, then it must be unique whenever the consumer’s preference relation is convex.
Substituting into p+q = 3=4, we achieve q = 1=2. Since the game is symmetric, we can derive exactly the same result for Player 1’s mixed action as well. Therefore, we get the mixed-strategy Nash equilibrium: both players choose Rock, Paper and Scissors with probabilities 1=4; 1=2; 1=4 respectively.
payoff) while M gives 1 irrespective of player 1’s strategy.
Therefore, M is eliminated by mixing L and R .
After eliminating M , we can further eliminate D (step 2) and L
(step 3), eventually picks up ( U , R ) as a unique outcome.