Question

(Specifically parts e-f, the rest is posted for context)

1.   (Ricardian Model, Chapter 2) Consider a Ricardian model of comparative advantage. There are two countries, China and the US. Each country can produce two goods, shoes (S) and food (F). Assume China has 600 workers and the US has 200 workers. Labor productivity in each country is:

Labor Productivity by Country and Good
   United States   China
Shoes   5 shoes/day   4 shoes/day
Food   15 bushels/day   4 bushels/day

a)   Which country has the absolute advantage in shoes?; in food? Explain.

i What is the opportunity cost of producing food in China?; in the U.S.? What is the opportunity cost of producing shoes in China?; in the U.S.?

b)   Derive and sketch the production possibility frontier for each country. Assume that, prior to trade, the
U.S. produces 500 shoes and 1,500 bushels of food, while China produces 1,200 shoes and 1,200 bushels of food. Show how it is possible, by altering production in each country, to increase total world output of both goods.

c)   In the absence of trade, what would autarky (no trade) relative prices be in each country? What would the real wage (in terms of each good) be in each country?

d)   If trade is allowed between the two countries, what will the pattern of trade be (i.e., what good will the US export and what good will it import), how does trade affect the real wage in each country and what can you conclude about the post-trade relative price of shoes?

e)   Assume all people have the same preferences. Let Df , Ds represent demand for goods F (food) and S (shoes), respectively. Assume people spend one-half their income on each good:
Df = I/2 x Pf ; Ds = I/2 x Ps ; where I (personal income) is the wage rate, and Ps , Pf are the prices
of the two goods. Total income (IUS for US and IChina for China) is the wage rate times the number of workers (Hint: use total income to compute a country’s total demand and start by assuming countries completely specialize. Is complete specialization by both countries an equilibrium? Explain your answer.).

i   Find the equilibrium world (relative) price of goods under free trade (i.e., set total world supply equal to total world demand and solve for price).

ii   Show how the real wage changes in each country due to free trade. Do both countries gain from free trade?

f)   Under free trade, how would a 15% increase in China's productivity in both sectors affect world prices and the real wage in the US and China? Explain. (a specific answer is required; use the demand curves from part (e) to find the new equilibrium relative price of shoes. Hint: start again by assuming that each country completely specializes. Is complete specialization still an equilibrium? Explain.).

Answer 1

Labour productivity

	united states	china
shoes	5	4
food	15	4

1] united states has a absolute advantage in both goods because labour productivity is higher than for us in both goods

i] opprtunity cost of producing shoes

in china = 4 / 4=1

in u.s.a =15 /5  = 3

the opportunity cost of producing food

in china =4 /4 =1

in u.s.a = 5 /15 =1/3

since opportuity cost of food is less for u.s a and opportunity cost of shoes is lower for china so china will produce  shoes and u.s.a will produce food  

given u.s. a =200

china =600

the total production of food =15 * 200 = 3000

the total production of shoes = 4 * 600 = 2400

increases in food = 3000 - [2700 ] = 300

increases in shoes = 2400 - [1700 ] = 700

c ] with no trade relative price

for the production in both sides wages in food = wages in shoes

p_f mp_p = p₅ mp₅

{p_f / p_s =mp_s / mp_f }

u.s.a = 5 / 15 = 1/3

in china = 4/4 = 1

d ] with trade u. s.a with exports food amd import shoes and vice versia for cina