Assume that a firm produces 90 units of output using 9 units of input X and 9 units of input Y. The.

Assume that a firm produces 90 units of output using 9 units of input X and 9 units of input Y. The firm’s technological possibilities can be represented by the production function Q ¼ 10X1=2Y1=2, whose marginal products are MPx ¼ Q 2X and MPy ¼ Q 2Y. a) If the price of X is $8 and the price of Y is $16, is the input combination of 9 units of X and 9 units of Y the most efficient way to produce 90 units of output? b) What must the ratio of input prices be for this input combination to be efficient? c) Assume that the price of X is $1 and the price of Y is $2. Derive the least-cost way to produce 400 units of output. (Hint: Remember that at an efficient input combination, the ratio of the marginal products—the marginal rate of technical substitution—equals the ratio of the input prices.