1. A firm's production function is qi = 10 Li^.3 Ki^.5.

a. Prove that the firm has decreasing returns to scale.

b. Theresa received an order for 5000 units. Find the optimal K/L ratio, as a function of w/r. Next, assuming w = $20 and r = .10, solve for Ki*, Li*, and qi*. Then draw a graph, showing the isoquant and isocost line associated with your answer.

c. If this firm had a budget of $80,000 to spend on inputs, how many units of output could be made? Continue to assume w = $20, and r = .10 as in part b. Again, draw a graph showing the relevant isocost line and isoquant at your solution point.

d. If the price of the output was $4, find the profit-maximizing level of Li, Ki, and qi