(a) Does this production function exhibit increasing, decreasing, or constant returns to scale? Justify your answer. (b) Find the cost-minimizing quantities of capital and labour for this firm as a function of r, w, and q (where q is the quantity to be produced). (c) Based on your answer in part (b), draw the firm's demand curve for capital input. Find the slope of the demand curve for capital. (d) Based on your answer in part (c), is the demand for capital, with respect to its own price, elastic or inelastic? Show your work and explain. (e) Suppose w=r= a which is a positive value. Derive the (long-run) total, average and marginal cost functions. (f) (g) How do average costs change when the output increases? Explain why this is the case by comparing marginal costs and average costs and provide an intuitive explanation. Write the equation of the (inverse) supply curve of this firm (with price P as a function of the quantity q). Draw this supply curve (with P in the vertical axis and q in the horizontal axis). (h) Suppose the market is perfectly competitive and it is comprised of 100 identical firms with the same production function of this question. The markets for capital and labour are also competitive and the equilibrium input prices are w = r = 50. The output market demand is Qd = 4200-60P (i) (ii) Compute the equilibrium market price and quantity. Compute the equilibrium quantity each firm will produce.
(a) Does this production function exhibit increasing, decreasing, or constant returns to scale? Justify your answer. (b) Find the cost-minimizing quantities of capital and labour for this firm as a function of r, w, and q (where q is the quantity to be produced). (c) Based on your answer in part (b), draw the firm's demand curve for capital input. Find the slope of the demand curve for capital. (d) Based on your answer in part (c), is the demand for capital, with respect to its own price, elastic or inelastic? Show your work and explain. (e) Suppose w=r= a which is a positive value. Derive the (long-run) total, average and marginal cost functions. (f) (g) How do average costs change when the output increases? Explain why this is the case by comparing marginal costs and average costs and provide an intuitive explanation. Write the equation of the (inverse) supply curve of this firm (with price P as a function of the quantity q). Draw this supply curve (with P in the vertical axis and q in the horizontal axis). (h) Suppose the market is perfectly competitive and it is comprised of 100 identical firms with the same production function of this question. The markets for capital and labour are also competitive and the equilibrium input prices are w = r = 50. The output market demand is Qd = 4200-60P (i) (ii) Compute the equilibrium market price and quantity. Compute the equilibrium quantity each firm will produce.
Chapter11: Profit Maximization
Section: Chapter Questions
Problem 11.9P
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Transcribed Image Text:Question 1
A firm's production function is
q=K+L
where q is the quantity of final production, K is the quantity of capital, and I is the quantity of
labour. Suppose that each unit of capital costs r and each unit of labor costs w.
(a)
Does this production function exhibit increasing, decreasing, or constant returns
to scale? Justify your answer.
(b)
Find the cost-minimizing quantities of capital and labour for this firm as a function
of r, w, and q (where q is the quantity to be produced).
(c)
Based on your answer in part (b), draw the firm's demand curve for capital input.
Find the slope of the demand curve for capital.
(d)
Based on your answer in part (c), is the demand for capital, with respect to its
own price, elastic or inelastic? Show your work and explain.
(e)
Suppose w = r = a which is a positive value. Derive the (long-run) total, average
and marginal cost functions.
(f)
(g)
How do average costs change when the output increases? Explain why this is the
case by comparing marginal costs and average costs and provide an intuitive explanation.
Write the equation of the (inverse) supply curve of this firm (with price P as a
function of the quantity q). Draw this supply curve (with P in the vertical axis and q in the
horizontal axis).
(h) Suppose the market is perfectly competitive and it is comprised of 100 identical firms with
the same production function of this question. The markets for capital and labour are also
competitive and the equilibrium input prices are w = r = 50. The output market demand is
Qd = 4200-60P
(i)
Compute the equilibrium market price and quantity.
Compute the equilibrium quantity each firm will produce.
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