Consider a firm that employs capital and labour and uses the production technology Q = min[K, L] (think of taxi cabs: you need exactly one car and one driver per taxi). Factor prices are r for capital and w for labour. a) Draw the isoquant for Q = 100. b) Does this production function exhibit increasing, constant, or decreasing returns to scale? Show/explain. c) What is the optimal relationship between K and L? What is the input demand for Labour (L as a function of Output) and the input demand for Capital? d) Derive the long-run cost function: (eg C = wL + rK where L and K are optimal choices). e) What is the long-run marginal and average cost function with r = 4 and w = 4? f) What is the cost of Q=100? Q= 200? g) Does this cost function exhibit increasing, constant, or decreasing economies of scale?
Consider a firm that employs capital and labour and uses the production
technology Q = min[K, L] (think of taxi cabs: you need exactly one car and one driver per taxi).
Factor prices are r for capital and w for labour.
a) Draw the isoquant for Q = 100.
b) Does this production function exhibit increasing, constant, or decreasing returns to
scale? Show/explain.
c) What is the optimal relationship between K and L? What is the input
(L as a function of Output) and the input demand for Capital?
d) Derive the long-run cost function: (eg C = wL + rK where L and K are optimal choices).
e) What is the long-run marginal and average cost function with r = 4 and w = 4?
f) What is the cost of Q=100? Q= 200?
g) Does this cost function exhibit increasing, constant, or decreasing economies of scale?
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