Suppose that a firm's production function is given by Q = KL. If capital is fixed at 1 unit in the short run, how much labor should the firm employ to maximize profits if the wage rate is $2? Assume that the price of product the firm sells is $10.

XYZ Co. operates in a competitive market. Its production function is q = L^α K^β . The firm takes the wage, rental rate and price as given. a) Derive the firm's conditional labor and capital demand functions. b) How does the firm react to an increase in the wage rate? c) Derive the firm's cost function.

Assume a firm has the following short-run production function: q(L) = L+6L2-1/2L3 If this firm is going to maximize profits in the short-run by producing a strictly positive level of output (q>0), what is the lowest level of labor (L) they would employ? A.) Minimum L=?

Suppose the short-run production function for a restaurant producing a pack of food is given by: Q = 3L – 0.312 Where Q is the number of packs of food produced and L is the amount of labour used. If the cost of a unit of labour is ¢6 and the unit price of a pack of food produced is ¢10, a) what is the amount of labour the restaurant should employ in order to maximize profit. b) How much profit is made?