Question

Consider a country, Home, populated by a labor force of 90 workers. The country can produce two goods, Apples and Bananas. Labor is the only factor of production and it can freely move across sectors. It takes 1/2 unit of labor to produce one Apple; similarly, and it takes 1/2 unit of labor to produce a Banana.

Notes:

If the country does not produce any bananas , then , it can produce (90)/(1/2) = 90(2) = 180 apples.

If the country does not produce any apples , then it can produce (90)/(1/2) = (90)(2) = 180 bananas.

The opportunity cost of producing an apple = 180/180 = 1 banana . And the opportunity cost of producing a banana = 180/180= 1 apple.

Questions:

1. Given a certain wage w that a worker in either sector earns and given that producers of Apples and Bananas are perfectly competitive, what is the relationship between the wage and the price of apples pA and between the wage and the price of Bananas pB?

2. What is the relative price pA/pB when the Home country is in autarky? In autarky, Apple producers that go to the market in the Home country with 5 Apples, can sell them for a certain number of Bananas, how many?

Answer 1

1. The wages of both the workers will be exactly the same. This is because the same amount of labour goes into the production of both the goods (i.e. 1/2 units of labour). This means that both the sectors will demand the same amount of labour to produce the same amount of goods. So, if personal heterogeneities and productivity of labourers in terms of producing apples and bananas are held constant, then the market demand for apples and bananas will be the only determining factor for the wage rate in both the sectors. Thus, any increase in the price of the product, whether apples or bananas, arising due to an increase in the demand for the product under constant supply conditions, will leas to a rise in the wage rate so that more labourers can be attracted to the production of that commodity over the other.

2. In autarky, the relative commodity prices is the opportunity cost of production. It means the number of units of one commodity that has to be given up tp produce one unit of another commodity. In this case, it is given that to produce one apple, one banana has to be given up, and vice versa. Thus, the relative commodity price pA/pB = 1

One apple can be sold for one banana in the market in such a case. So, if the producer goes to the market with 5 apples, she can sell it for 5 bananas.