A firm’s production function is Q = 10 + 30L - .5L2+ 30K – K2, and its competitive demand function is PQ= MRQ = d = $40. The prices of L and K are PL = $6 and PK= $12. Suppose K is fixed at K =10.  Use Excel Solver or otherwise to find the profit-maximizing quantity (Q).

Suppose a firm uses a single input to produce a single output according to a production function f(x) = 10√x where x is the number of units of input. The output initially sells for £120 per unit. The input costs £20 per unit. A change in the market causes the product price to increase from £120 per unit to £200 per unit, all else equal. How does this change in product price affect the firm's profit maximizing level of profits? a. Profits increase by £16,000 Ob. Profits do not change Profits increase by £8,000 d. None of the other answers is correct Profits increase by £9,000 f. Profits increase by £18,000 g. Profits increase by £50,000 h. Profits increase by £32,000 C. e.

A firm’s production function is Q = 10 + 30L - .5L2+ 30K – K2, and its competitive demand function is PQ= MRQ = d = $40. The prices of L and K are PL = $6 and PK= $12. Suppose K is fixed at K =10.  Use Excel Solver to find the profit-maximizing quantity (Q).   A. 660.   B. 684.   C. 764.   D. 788.   E. 864.

On the graph input tool, change the number found in the Quantity Demanded field to determine the prices that correspond to the production of 0, 6, 12, 15, 18, 24, and 30 units of output. Calculate the total revenue for each of these production levels. Then, on the following graph, use the green points (triangle symbol) to plot the results.   Calculate the total revenue if the firm produces 6 versus 5 units. Then, calculate the marginal revenue of the sixth unit produced. The marginal revenue of the sixth unit produced is________.   Calculate the total revenue if the firm produces 12 versus 11 units. Then, calculate the marginal revenue of the 12th unit produced. The marginal revenue of the 12th unit produced is_________.