Derive profit function based on the Cobb-Douglas production function 1/3 2/3 of y = x x,

Explain the relationship between the production function and the average costs and marginal costs curve of a firm.

A firm has a production function q = min [L-OKO.6, 2M] (à) Find the firm's optimality condition for its factor mix of K and L given that it wants to produce amount q* of output. (b) Calculate the firm's long run cost function C(q) and interpret it. (c) If all firms in a particular industry have this production function, what would this imply about the viability of long run competitive equilibrium?

A firm has the following Cobb-Douglas production function:         q=(L^α)(K^1-α)0<α < 1 is a parameter. Suppose in the short run K = 1. The rental rate of a unit of K is $10, and the wage rate of a unit of L is $20.(a) Derive the marginal cost of the firm (expressed in terms of α and q).(b) Derive the average variable cost of the firm (expressed in terms of α and q).(c) Derive the cost function of the firm.

Find out the maximum possible output for a firm with two units of L and 50 units of k when its production function is Q = 5L + 3K