3. A production function for a firm is given by Q = 20K 0.7L0.3 The cost...

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3. A production function for a firm is given by Q = 20K 0.7L0.3 The cost of unit K is Pk = $20 and the cost of unit L is PL = $5, and the firm has the budget of $400 for production. (i) Determine the optimal resource employments (K, L) that give max- imum output within the budget (specify the 1st order conditions). (ii) Specify the values for the Lagrange multiplier and the maximum output. (iii) Show that at the optimal resource employments, the following equal- ity holds MPK MPL PL 3. A production function for a firm is given by Q = 20K 0.7L0.3 The cost of unit K is Pk = $20 and the cost of unit L is PL = $5, and the firm has the budget of $400 for production. (i) Determine the optimal resource employments (K, L) that give max- imum output within the budget (specify the 1st order conditions). (ii) Specify the values for the Lagrange multiplier and the maximum output. (iii) Show that at the optimal resource employments, the following equal- ity holds MPK MPL PL