Soundscape Enterprises manufactures Sonoblast, a device that produces a high-pitched reminder to telemarketers that they have once again disturbed you just when you were sitting down to dinner. The production function for Sonoblasts is given by the formula Q=2KL12/ where Q is in units of output per period, K is in machine-weeks per period, and L is in labour-weeks per period. The machine rental rate r is $512 per machine-week and the wage rate w is $128 per labour-week. In the short run, K is fixed at 4 machine-weeks per period.

a. Give the formulas for the short-run production function and the marginal product of labour (MPL) function.

b. Express variable cost (VC), total cost (TC), and marginal cost (MC) as functions of L and as functions of Q; and average variable cost (AVC), average fixed cost (AFC) and average total cost (ATC) as functions of Q.

c. At what level of Q is ATC minimized? What are the values of ATC and of MC at this level of output?

d. If K is increased to a fixed 16 units, at what level of Q is ATC minimized, and what are the values of ATC and of MC at this level of output?

e. In the long run, with all inputs variable, what is the optimal K/L ration with input prices unchanged? How many units of L and of K would be required to produce the levels of output in 1c and in 1d and what is the average cost of producing Sonoblasts in each case? Explain the relation between your results here and those for 1c and 1d.