# ECON 561 San Diego State University Specific Factors Model Exam

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ECON 561 Exam 2 – Fall 2021
1. Short Answer Questions (10 points)
(a) Briefly explain why the Specific Factors Model is considered as a short-run model compared with the
Heckscher-Ohlin model.
(b) Breifly explain why the PPF is curved for both the Specific Factors Model and Heckscher-Ohlin Model.
(c) Suppose the US is a more capital-abundant economy than China. Between workers and capital owners,
who would you expect the trade war to be more harmful to? Why? (you have to apply the Stolper-Samuelson
Theorem to get full points)
(d) True or false. In the Specific Factors Model, if the minimum wage is set below the market equilibrium wage,
then there will be no unemployment generated by this minimum wage policy.
(e) True of false. The relative price is the only changed condition after the market integration in all neo-classical
frameworks. (hint: meaning all the other variables are affected by the change in relative price)
2. The Specific Factors Model (25 points)
Suppose there are two countries, Home and Foreign. Both countries produce iPhone and Steel. The production
of iPhone requires capital (K) skilled labor (H). The production of Steel requires capital (K) and unskilled labor (L).
The two countries have the following production functions for iPhone and Steel: (pay extra attention, capital is
the mobile factor here!)
Qiphone = K1/2 H 1/2 ; Qsteel = K1/2 L1/2
Factor Endowment Stock at Home and Foreign:
Home: capital (K home ) =600, skilled labor (H home ) = 500, unskilled labor (Lhome ) = 100
Foreign : capital (K f oreign ) =1000, skilled labor (H f oreign ) = 800, unskilled labor (L f oreign ) = 200
 (2 points) (show your steps and reasoning) Does the production function for iPhone exhibit constant, increasing, or decreasing returns to scale with respect to
 Capital (K) only?
 Both capital (K) and High-skilled labor (H)?
 (2 points) Calculate the marginal of capital (MPK) for both iPhone and Steel.
 (4 points) Suppose home autarkic prices for iPhone and Steel are p I and pS , and p I = pS = 1. Calculate the
rental rate equilibrium and capital allocation for home country.
 (2 points) Suppose foreign autarkic prices for iPhone and Steel are p0I and p0S , and p0I = p0S = 1. Calculate
the rental rate equilibrium and capital allocation for foreign country.
 (5 points) Draw the Butterfly Graph for the Home country. Then, without any calculation, by inspecting
the autarkic relative price of iPhones at Home and Foreign, can you make any conjecture on their trade
pattern if the two countries were to engage in free trade with each other? (Lable all x and y axis)
p
 (5 points) Graphically show the aggregate gains from trade for Home country. ( p I < S the world relative price. pW I pW S < p0I ), p0S where pW I pW S is  (5 points) Based on the above relative price inequality, analyze the distribution effect of free trade at Home. More specifically, point out the winners and losers (capital owners, skilled labor, unskilled-labor) after trade at Home using the Scissors graph. Then disucss and draw the impact of foreign direct investment (inrease in K) on returns to capital, skilled and unskilled labor. 1 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 (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 ; Q F = K F2 L F2  (20 points) Solve the firms profit maximization problem for both car and food industry. Use ?C , ? F to represent the firms profit in the car and food industry respectively. Product prices for cars, food are: p I, 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: wr , x-axis: KL ).  (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: pW C pW F >
pUS
C
.
pUS
F
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 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 Q F , 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:
y = L? K ? H ?
 (10 points) 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?)
 (10 points) now suppose another production function is given as:
g = L? + K ? + H ? + H
where ? + ? + ? = 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 exogenous). As the owner of the firm, write down the firms profit maximization problem (using the first
production function, y = L? K ? H ? ). Drivie first-order condistion, and then, solve the firms optimal production equilibrium (aka solving for L? , K ? , H ? ) if the total starting investment money=\$1000.
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