(a) Nkrumah Clothing Limited produces its output using a Cobb-Douglas production function of the form: Y = KaL¹-a 0 < a < 1. If the company's price is fixed in the short-run; that is, it takes both the price of its product, P, and the quantity. Y, as given. Factor prices are competitive; thus, the company takes the wage, W, and the rental price of capital, rk, as given. What is the company's choice of labour (L) given P. Y, W, and K? Given your answer in (i), what is the company's profit as a function of P, Y. W, and K? i. ii. iii. iv. where Find the first-order condition for the orofit-maximising choice of K. Is the second-order condition satisfied? Solve the first-order condition in (iii) for K as a function of P, Y, W, and T- How, if at all, do changes in each of these variables affect K?

(a) Nkrumah Clothing Limited produces its output using a Cobb-Douglas production function of the form: Y = KaL¹-a 0 < a < 1. If the company's price is fixed in the short-run; that is, it takes both the price of its product, P, and the quantity. Y, as given. Factor prices are competitive; thus, the company takes the wage, W, and the rental price of capital, rk, as given. What is the company's choice of labour (L) given P. Y, W, and K? Given your answer in (i), what is the company's profit as a function of P, Y. W, and K? i. ii. iii. iv. where Find the first-order condition for the orofit-maximising choice of K. Is the second-order condition satisfied? Solve the first-order condition in (iii) for K as a function of P, Y, W, and T- How, if at all, do changes in each of these variables affect K?

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

(a) Nkrumah Clothing Limited produces its output using a Cobb-Douglas production
function of the form:
Y = KaL¹-a
0 < a < 1.
If the company's price is fixed in the short-run; that is, it takes both the price of its
product, P, and the quantity. Y, as given. Factor prices are competitive; thus, the
company takes the wage, W, and the rental price of capital, rg, as given.
What is the company's choice of labour (L) given P. Y, W, and K?
Given your answer in (i), what is the company's profit as a function of P, Y.
W, and K?
i.
where
ii.
iii.
Find the first-order condition for the orofit-maximising choice of K. Is the
second-order condition satisfied?
iv. Solve the first-order condition in (ili) for K as a function of P, Y, W, and T-
How, if at all, do changes in each of these variables affect K?
(b) Distinguish between financial investment and real investments.
C

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