1. A competitive firm has a production function described as follows. Weekly output is the square root of the minimum of the number of units of capital and the number of units of labor employed per week" Suppose that in the short run this firm must use 16 units of capital but can vary its amount of labor freely. a. Write down a formula that describes the marginal product of labor in the short run as a function of the amount of labor used. (Be careful at the boundaries.) b. If the wage is w=$1 and the price of output is p =$4, how much labor will the firm demand in the short run? c. What if w =$1 and p= $10? 2. The production function for good y is y = max (10x1, 4x2), where x1 and x2 are the amounts of factors 1 and 2. Find the cost function for good y. 3. If the production function for tuna casseroles is min( x1,x2 2), where x1 is the amount of factor 1 and x2 is the amount of factor x2, find the cost function for tuna casseroles. 4. A competitive firm has the short-run cost function c(y) =)3-2)2 + 5y +6. Write down equations for: a. The firm's average variable cost function b. The firm's marginal cost function c. At what level of output is average variable cost minimized