Suppose that the monthly output of bicycles is characterized by q = 20(KL)^1/2, where K is the capital used in production and L is the number of worker hours employed. MPL = 10(K/L)^1/2 and MPK = 10(L/K)^1/2.
a) Graph the isoquant with 2,000 bicycles.
b) How many units of capital firm has to employ to produce 2,000 bicycles, if firmemploys 100 units of labour? How many units of capital firm has to employ toproduce 2,000 bicycles, if firm employs 101 units of labour? What is theapproximate value for the MRTS at L= 100?
c) Compare the result from past b) with MRTS calculated using a formula.
Assume price of labour is w and price of capital is r.
d) Derive conditional demand for labour and capital. Derive minimized total cost.
e) Derive the equation of firm's expansion path. Draw the expansion path.
f) Suppose both wages and rental rate double. How would this affect the firm's expansion path? How would long-run average and marginal cost be affected?What can you conclude about the effect of uniform inflation of input costs on the costs of bicycle production?
g) Suppose wages rise doubles but rental rate stay fixed. How would this affect the firm's expansion path? How would this affect the long-run average and marginal cost of bicycle production? Why does a doubling of the wage result in a much smaller increase in average costs?
Assume that technical progress shifted the production function to ???? = 40√????????, that is all of the input combinations identified earlier can now produce 4,000 bicycles per year.
h) Would the value calculated for the MRTS in parts b) and c) be changed as a result of this technical progress, assuming now that the MRTS is measured along the q =4,000 isoquant? i) Assuming this shift does not change the cost- minimizing expansion path, how are long-run total, average, and marginal costs affected?