Question

The U.S. produces 6 buschels of wheat in 1 labor hour and 3 yards of cloth in 1 labor hour. The U.K. producers 1 bushel of wheat in 1 labor hour and 2 yards of cloth in 1 labor hour. Assume the wage rate per labor-hour is $6 in the U.S. and £1.8 in the U.K. 1) Which commodity will the U.S. import and export if the exchange rate between the $ and the £ is £1=$1? 2) When will trade be balanced between the U.S. and U.K.?

Answer 1

a. Given information can be summarized as

	US	UK
Wheat (bushel/labor hour)	6	1
Cloth (yard/labor hour)	3	2

Now ,

Exchange rate given is £1=$1. So cost wise data can be summarized as ( in cost per unit).

	US	UK
Wheat (dollar/bushel)	1	1.8
Cloth (dollar/yard)	2	0.9

The above table is populated as

6 bushels of wheat is produced in US in 1 labor hour and wage rate in 6$ per labor hour. So bushels of wheat per dollar = 6 dollars /6 bushels = 1 dollar/bushel.

Similarly, In US 3 yards of cloth in 1 labor hour and wage rate in 6$ per labor hour. So yards of cloth per dollar =6 dollars / 3 yards= 2 dollar/yard.

Now for UK, and exchange rate is £1=$1. No difference between $ and £

1 bushels of wheat is produced in UK in 1 labor hour and wage rate in 1.8$ per labor hour. So bushels of wheat per dollar = 1.8 dollar/1 bushel = 1.8 dollar/bushel

2 yards of cloth in 1 labor hour and wage rate in 1.8$ per labor hour. So bushels of wheat per dollar = 1.8 dollar/2 yards = 0.9 dollar/yard .

So we see that cost of production of wheat is cheap in US than in UK and cost of production of cloth is cheap in UK than in US. So, US exports wheat and imports cloth while UK exports cloth and imports wheat.

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b. again constructing a table for domestic exchange ratios for US and UK in the absence of trade.

	US	UK
Wheat: Cloth	1:2 = 1:2	1.8 : 0.9 = 1:0.5
Cloth: Wheat	2:1 = 1:0.5	0.9 : 1.8 = 1: 2

Under no trade condition we see that in UK 1 £ worth of wheat is exchanged at 0.5 £ worth of cloth .

Similarly in US under no trade condition 1 $ worth of cloth is exchanged at 0.5 $ worth of wheat.

Now under given exchange rate i.e. £1=$1, both the countries will exchange 1 $ worth of wheat to 1 $ worth of cloth.

The gain to UK will be 1- 0.5 = 0.5$ worth of wheat, and

The gain to US will be 1- 0.5 = 0.5$ worth of cloth

Under these exchange conditions the trade will be balanced between US and UK .