Write down the profit maximization problem faced by firm

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Alice owns a firm which produces oranges. Alice needs only two types of inputs which we call capital denoted by K and labor denoted by L. Price of capital i.e. the rental rate is r and price of labor i.e. wage rate is w. Each orange sells for p dollars per unit. The technology available to Alice can be represented by the following Cobb Douglas production function f (K, L) = KaL b , where a, b are positive. He chooses a combination of output, labor and capital denoted by y, L and K respectively to maximize profits. Marginal product of labor MPL = bKaL b−1 and marginal product of capital is MPK = aKa−1L b

1. Write down the profit maximization problem faced by Alice’s firm

2. What conditions should Alice’s chosen bundle i.e. (y, K, L) satisfy

3. Solve for the optimal K and L in terms of (a, b, p, w, r)

4. Solve for optimal y in terms of (a, b, p, w, r

Reference no: EM131009717

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