8. [5 points] Consider a Firm producing a given output in the long run; the inputs employed in production are labour L, which costs w > 0 per unit, and capital K, which costs r> 0 per unit. The Firm produces a quantity Q according to the following production function: Q(K, L) = 4K²/3L\/3_ Suppose the Firm's target is to produce 1,000 (Q = 1,000). (a) Find the cost-minimising combination of inputs K* and L when w = 80 and r = 160, then compute the corresponding long-run cost of production. (b) Suppose that the rental price of capital decreases to r' = 20. Find the new cost-minimising input combination. (c) Use your answers to points a) and b) to calculate the firm's price elasticity of demand for capital over this range of prices (rounded to two digits).

8. [5 points] Consider a Firm producing a given output in the long run; the inputs employed in production are labour L, which costs w > 0 per unit, and capital K, which costs r> 0 per unit. The Firm produces a quantity Q according to the following production function: Q(K, L) = 4K²/3L\/3_ Suppose the Firm's target is to produce 1,000 (Q = 1,000). (a) Find the cost-minimising combination of inputs K* and L when w = 80 and r = 160, then compute the corresponding long-run cost of production. (b) Suppose that the rental price of capital decreases to r' = 20. Find the new cost-minimising input combination. (c) Use your answers to points a) and b) to calculate the firm's price elasticity of demand for capital over this range of prices (rounded to two digits).

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

8. [5 points] Consider a Firm producing a given output in the long run; the inputs employed in production
are labour L, which costs w > 0 per unit, and capital K, which costs r > 0 per unit. The Firm produces
a quantity Q according to the following production function:
Q(K, L)
= 4K²/³L\/3_
Suppose the Firm's target is to produce 1,000 (Q = 1, 000).
(a) Find the cost-minimising combination of inputs K* and L* when w = 80 and r = 160, then
compute the corresponding long-run cost of production.
(b) Suppose that the rental price of capital decreases to r' = 20. Find the new cost-minimising input
combination.
(c) Use your answers to points a) and b) to calculate the firm's price elasticity of demand for capital
over this range of prices (rounded to two digits).

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