The Hecksher-Ohlin Model

Suppose there are two countries, US and Mexico (two countries). Both countries produce cars and food (two sectors). The production of cars requires capital (K_C) labor (L_C). The production of food also requires Capital (K_F) and labor (L_F) (two factors). The two countries have the following production functions for cars and food:

2 ______1 ________________________ 1________1

QC = KC3 LC3 ; QF = KF2 LF2

• Solve the firms profit maximization problem for both car and food industry. Use _C, _F to represent the firms profit in the car and food industry respectively. Product prices for cars, food are: p_I,p_S. Factor prices for labor and capital are: w, r. Derive the first-order conditions for both profict functions with repect to both factors (labor and capital). Then derive the wage/rental ratio as the function of labor/capital ratio, and draw them graphically. (y-axis: ^w_r , x-axis: _K^L ).
• Based on the above calculation. Which sector is the capital intensive sector. Suppose US is a capital abundant country compared with Mexico. How do you predict the trade patterns between US and Mexico? Which theorem would you use? (hint: not those two post-trade theorems you might think)
• Given the following inequatlity between the world relative price and the domestic relative price: p^pW^WCF ^{> p}p^US_US^CF . Which factor in the US will win or lose after trade? Which theorem should one use to answer the

question? (y-axis: Food Q_F, x-axis: Cars Q_C)

• Rybczynski Theorem Graph. Suppose a large influx of immigration filled up the labor market in the US which leads to a huge increase in the total labor endowment. Draw the PPF and show how the production reallocation happens regarding this immigration inflow in the short run. (y-axis: Food Q_F, x-axis: Cars Q_C). Clearly label the before/after trade PPF curves, productions in both sectors, and the relative price.

PART 2

Production Function and Firms Problem

Suppose a production function is given as:

y = LKH

• where, L=labor, K=capital, H=leadership, and ++= 1, derive the marginal product of labor, capital, and leadership respectively, and find the returns to scale for all factors, and each factor respectively. (constant, increasing, or decreasing? why?)
• now suppose another production function is given as:

g = L+K+H+H

where ++= 1, whats the returns to scale with respect to L, K, and H repsectively? (constant, increasing,

or decreasing? why)

Suppose the factor returns to L, K, and H are w,r, and b; the price of the product y is p (all exogenous). As the owner of the firm, write down the firms profit maximization problem (using the first production function, y = LKH). Drivie first-order condistion, and then, solve the firms optimal production equilibrium (aka solving for L, K, H) if the total starting investment money=$1000.

3. The Hecksher-Ohlin Model (35 points) Suppose there are two countries, US and Mexico (two countries). Both countries produce cars and food (two sectors). The production of cars requires capital (Kc) labor (LC). The production of food also requires Capital (KF) and labor (LF) (two factors). The two countries have the following production functions for cars and food: Qc = KLS; Q== KL (20 points) Solve the firm's profit maximization problem for both car and food industry. Use ac, Tlf to represent the firm's profit in the car and food industry respectively. Product prices for cars, food are: P1,Ps. Factor prices for labor and capital are: w,r. Derive the first-order conditions for both profict functions with repect to both factors (labor and capital). Then derive the wage/rental ratio as the function of labor/capital ratio, and draw them graphically. (y-axis: * , x-axis: k). (5 points) Based on the above calculation. Which sector is the capital intensive sector. Suppose US is a capital abundant country compared with Mexico. How do you predict the trade patterns between US and Mexico? Which theorem would you use? (hint: not those two post-trade theorems you might think) (5 points) Given the following inequatlity between the world relative price and the domestic relative price: pa Which factor in the US will win or lose after trade? Which theorem should one use to answer the question? (y-axis: Food QF, X-axis: Cars Qc) (5 points) Rybczynski Theorem Graph. Suppose a large influx of immigration filled up the labor market in the US which leads to a huge increase in the total labor endowment. Draw the PPF and show how the production reallocation happens regarding this immigration inflow in the short run. (y-axis: Food QF,x-axis: Cars Qc). Clearly label the before/after trade PPF curves, productions in both sectors, and the relative price. 4. Production Function and Firm's Problem (30 points) Suppose a production function is given as: pus PA y = LKPHY (10 points) where, L=labor, K=capital, H=leadership, and a +B+ y = 1, derive the marginal product of labor, capital, and leadership respectively, and find the returns to scale for all factors, and each factor respectively. (constant, increasing, or decreasing? why?) (10 points) now suppose another production function is given as: g= L* + KB + H7+H where a + B+7= 1, what's the returns to scale with respect to L, K, and H repsectively? (constant, increasing, or decreasing? why) (10 points) Suppose the factor returns to L, K, and H are w,r, and b; the price of the product y is p (all ex- ogenous). As the owner of the firm, write down the firm's profit maximization problem (using the first production function, y = LKBH). Drivie first-order condistion, and then, solve the firm's optimal produc- tion equilibrium (aka solving for L*,K*, H*) if the total starting investment money=$1000. 3. The Hecksher-Ohlin Model (35 points) Suppose there are two countries, US and Mexico (two countries). Both countries produce cars and food (two sectors). The production of cars requires capital (Kc) labor (LC). The production of food also requires Capital (KF) and labor (LF) (two factors). The two countries have the following production functions for cars and food: Qc = KLS; Q== KL (20 points) Solve the firm's profit maximization problem for both car and food industry. Use ac, Tlf to represent the firm's profit in the car and food industry respectively. Product prices for cars, food are: P1,Ps. Factor prices for labor and capital are: w,r. Derive the first-order conditions for both profict functions with repect to both factors (labor and capital). Then derive the wage/rental ratio as the function of labor/capital ratio, and draw them graphically. (y-axis: * , x-axis: k). (5 points) Based on the above calculation. Which sector is the capital intensive sector. Suppose US is a capital abundant country compared with Mexico. How do you predict the trade patterns between US and Mexico? Which theorem would you use? (hint: not those two post-trade theorems you might think) (5 points) Given the following inequatlity between the world relative price and the domestic relative price: pa Which factor in the US will win or lose after trade? Which theorem should one use to answer the question? (y-axis: Food QF, X-axis: Cars Qc) (5 points) Rybczynski Theorem Graph. Suppose a large influx of immigration filled up the labor market in the US which leads to a huge increase in the total labor endowment. Draw the PPF and show how the production reallocation happens regarding this immigration inflow in the short run. (y-axis: Food QF,x-axis: Cars Qc). Clearly label the before/after trade PPF curves, productions in both sectors, and the relative price. 4. Production Function and Firm's Problem (30 points) Suppose a production function is given as: pus PA y = LKPHY (10 points) where, L=labor, K=capital, H=leadership, and a +B+ y = 1, derive the marginal product of labor, capital, and leadership respectively, and find the returns to scale for all factors, and each factor respectively. (constant, increasing, or decreasing? why?) (10 points) now suppose another production function is given as: g= L* + KB + H7+H where a + B+7= 1, what's the returns to scale with respect to L, K, and H repsectively? (constant, increasing, or decreasing? why) (10 points) Suppose the factor returns to L, K, and H are w,r, and b; the price of the product y is p (all ex- ogenous). As the owner of the firm, write down the firm's profit maximization problem (using the first production function, y = LKBH). Drivie first-order condistion, and then, solve the firm's optimal produc- tion equilibrium (aka solving for L*,K*, H*) if the total starting investment money=$1000