Question

Suppose we have assumptions that allow us to utilized a H-O model to analyze the implications of trade between two countries, Home and Foreign. Their pre-trade capital stock and number of workers and allocations to each industry are given in the table below

	Home		Foreign
	Widgets	Fizzy	Widgets	Fizzy
K	4 million	1 million	1.5 million	0.5 million
L	2million	8 million	1 million	2 million

Capital and labor are both mobile across industries, and are used to produce both goods widgets and fizzy. We also know that in both countries production is based on constant returns to scale technology and widget production is capital intensive and fizzy is labor intensive. If in foreign the pre trade price of widgets is $2 and for fizzy it is $2. The pre trade wage is $10; and the pre trade rental to capital is $20. If post trade the price of widgets in foreign increases to $4 while the price of fizzy stays the same. Determine numerically the impact of trade on the welfare of all owners of factors in foreign, if foreign produces pre-trade 2 million widgets and 4 million fizzy.

What is the foreign post trade rental to capital? post trade wage?

Answer 1

Since the prices and wages of the pre trade of home are not given , we find the relative price of widgets in foreign which is :

(price of widgets in foreign/ price of fizzy in foreign) which is $2/$2=1.

now we see the wage rental ratio which is( wages in foreign/ rental capital )=$10/$20=0.5

since the wage rental ratio is less than relative price ratio , foreign specialises in widgets production.

The k/l ratio is given as follow :

home :widget =4/2=2 ; fizzy =1/8=0.125

foreign : widget =1.5/1=1.5; fizzy =0.5/2=0.25

this implies that foreign has comparative advantage in producing widgets while home has in fizzy production.

As per the table given , we know that even in the pre trade , both countries were producing both the goods. so when the international trade comes into play , due to competition , each sector will ensure that the price of each good is equal to the cost of production. Also the cost of producing a good depends on its faactor prices, so if wages rise , other things equal , the price of the good would increase and vice versa.

also after the trade since foreign has comparative advantage in production of widgets , it specialises in the production and the demand for capital increases since widgets is capital intensive. on the other hand we assume that since home specialises in production of fizzy , during the trade the demand for the labour would increase in the home which leads to reduced labour force in the foreign .

so the post trade relative price ratio of widget will be $4/$2= 2 which implies that the wage to rental ratio would also increase. this would aalso be because since we would have more demnd for capital in foreign the rental to capital would reduce .

since home has higher labour to capitaal ratio , it is labour abundant. so it will produce more fizzy which implies that home would have higher supply of fizzy. so home becomes exporter of fizzy and foreign becomes exporter of widgets.

a rise in price of widget would rasie the purchasing power of capital in both goods . this would make capital owners better off in foreign .

also we know that

wages= mpl*price where mpl is the marginal product of labour . so mpl = wages / price. = 10/2 = 5. if we ssume that mpl remians the same , then wages after trade would be mpl* price =5 * 4= 20 $ for widgets

\for fizzy after trade = 5*2=10 $

mpk would be 20/2=10 . ((marginal product of capital )

for capital rental c = price* mpk (marginal product of capital ) = 10*2=20$ for fizzy after trade

for widget =4* 10= 40$ after trade

so capital owners would be well off after the trade. and the labour in the wiget sector but eventiually there would be equalisation of wages and the incomes would be same in both home and foreign.