Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

In this assignment, you will solve a version of the specific factors model to see how trade can create both winners and losers through its

image text in transcribedimage text in transcribedimage text in transcribed
In this assignment, you will solve a version of the specific factors model to see how trade can create both winners and losers through its effects on real factor incomes. There is a single country, Home, and two sectors, 1 and 2. Home is endowed with L units of labor, K1 units of capital specific to sector 1, and K2 units of capital specific to sector 2. Household preferences in Home are Cobb-Douglas with potentially asymmetric weights: U (C1, C2) = CFC2-5 where C1 and C2 denote the household's consumption of goods 1 and 2 respectively. The parameter S E (0, 1) measures how much the household likes good 1 relative to good 2. The production technology available is the same in each sector, and is given by the following Cobb-Douglas production function: Xi = KI-LA where Xi, Ki, and L: denote the output, capital input, and labor input of sector i respectively. The parameter A E (0, 1) measures how important labor is for production relative to capital. In what follows, assume that factor endowments are: L = 1 K1 = 1 K2 = 1 and that the weight on labor in the production function is A = 2. We will examine how different values for the parameter S affect the welfare gains from trade.First1 we will solve {or demand and supply assuming that the goods prices pl and p2 (and hence the relative price p, E plg'pg) are known. Let w, n, and 1-; denote the wage, rental rate of sector 1 capital. and rental rate of sector 2 capital respectively. Demand The utility maximization problem for a household with income I is: 3 15 mstl 2 01,63 E-t- 13101 +1920: = 1' (a) What in equilibrium relative consumption, 0, E 01,102. given goods prices? Supply The prot maximization problem for a rm in sector a.' is: max{piKi1\"'L? 11K; till-4} Kola [b] Write down the rst-order conditions for this problem. Now note that capital market clearing requires: K; = K} for i E {1,2}. (c) \\Vhat is the equilibrium relative allocation of labor across sectors, L, E L1,.'IL2. given goods prices? (ti) What is equilibrium relative output, X, E Xu'Xg, given goods prices? Antarky Now suppose that Home is in autarky. Goods market clearing therefore requires that consumption equals production: 04 = X; for i E {1, 2}. (e) What is the equilibrium relative goods price p, in autarky? How does the relative price change with 3? Why? Now note that labor market clearing also requires: L1 + L: = E. (I) What is the allocation or labor in each sector, L1 and L2? ' ' ' E E El. EL :1 29 [5) What are real I'actor Incomes in terms of goods 1 and 2, Le. m , m\" 131' 19: , 91' and m' Trade Now suppose that Home can trade with the rest of the world at some prices - and suppose that the world relative price is p, E ppg" = 1. [11) Repeat your calculations in parts (fl(g) to determine real factor incomes under trade. (1) How does trade aect real factor incomes for (i) workers, (ii) owners of sector 1 capital, and (iii) owners of sector 2 capital? (Hint: your answer will depend on whether S

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Managerial Economics and Business Strategy

Authors: Michael R. baye

7th Edition

978-0073375960, 71267441, 73375969, 978-0071267441

More Books

Students also viewed these Economics questions

Question

How should a firm decide what industry it is in? Discuss.

Answered: 1 week ago