Miranda is stranded on a desert island, and having quite the enterprising spirit, notices that the oceans are teeming with fish and immediately seizes upon this lucrative opportunity. She is endowed with a single fishing net, but is unable to make any more, so that her capital stock remains fixed at = 1. Hence the number of fish q she catches depends only on the hours of labor that she employs, by the production function q = f(k, l)=√√kl= √t Let the rental rate of capital be v = 0, the wage rate be normalized to w = 1, and let p denote the price of fish. a) Find Miranda's cost function c(q). (b) Write Miranda's profit maximization problem and state the first order condition. (c) Find Miranda's output supply qS(p), labor demand lc(p), and profit π(p) as functions of the price of fish.
Miranda is stranded on a desert island, and having quite the enterprising spirit, notices that the oceans are teeming with fish and immediately seizes upon this lucrative opportunity. She is endowed with a single fishing net, but is unable to make any more, so that her capital stock remains fixed at = 1. Hence the number of fish q she catches depends only on the hours of labor that she employs, by the production function
q = f(k, l)=√√kl= √t
Let the rental rate of capital be v = 0, the wage rate be normalized to w = 1, and let p denote the price of fish.
a) Find Miranda's cost function c(q).
(b) Write Miranda's profit maximization problem and state the first order condition.
(c) Find Miranda's output supply qS(p), labor demand lc(p), and profit π(p) as functions of the price of fish.
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