Question

Graphing An average worker in Brazil can produce an ounce of soybeans in 20 minutes and an ounce of coffee in 60 minutes, while an average worker in Peru can produce an ounce of soybeans in 80 minutes and an ounce of coffee in 120 minutes. Suppose each worker has 480 total minutes to produce coffee and soybeans. (i) Draw PPF's for Brazil and Peru. Please put coffee on the Y-axis. (ii) Suggest a mutually beneficial term of trade between the two countries. (iii) On the same graphs as part (i), draw CPF's consistent with your answer in part (ii)

Answer 1

1) For Brazil , if all resources (here time) are used to produce only soybeans then the amount of soybeans produced will be 480/20 = 24 ounces.

If all resources (here time) are used to produce only coffee then the amount of coffee produced will be 480/60 = 8 ounces.

Without trade Brazil might produce equal amounts of both soybeans and coffee. As such, it will use 120 mins of labor in producing soybeans i.e, it will produce 120/20= 6 ounces of soybeans and it will use 360 mins of labor in producing coffee i.e, it will produce 360/60 = 6 ounces of coffee. The Production Possibility Frontier curve for Brazil can be drawn by joining all these points.

For Peru, if all resources (here time) are used to produce only soybeans then the amount of soybeans produced will be 480/80 = 6 ounces.

If all resources (here time) are used to produce only coffee then the amount of coffee produced will be 480/120=4 ounces.

Without trade Peru might produce equal amounts of soybeans and coffee. As such, it will use 192 mins of labor in producing soybeans or it will produce 192/80 = 2.4 ounces of soybeans and it will use 288 mins of labor in producing coffee or it will produce 288/120=2.4 ounces of coffee. (The time values can be known by solving equations X+Y=480 and X/80 = Y/120). The Production Possibility Frontier curve for Peru can be drawn by joining all these points.

2) For terms of trade , opportunity cost for each item needs to be calculated.

For Brazil, opportunity cost for producing soybeans is 60/20=3

and opportunity cost for producing coffee is 20/60 =1/3

Similarly, for Peru , opportunity cost for producing soybeans is 120/80 = 3/2

and opportunity cost for producing coffee is 80/120 = 2/3

Thus, opportunity cost for producing soybeans is lower for Brazil (Quantity produced is inversely proportionate to time) and opportunity cost for producing coffee is lower for Peru (Quantity produced is inversely proportionate to time).

Hence, Brazil has comparative advantage in producing soybeans while Peru has comparative advantage in producing coffee.

Hence, Brazil will specialize and sell soybeans to Peru and Peru will specialize and sell coffee to Brazil.

3) With trade , Brazil will produce 24 units of soybeans and Peru will produce 4 units of coffee.The terms of trade for soybean must be in between 3/2 and 3. Suppose the terms of trade for soybeans be 2 or two units of soybeans will be exchanged for an unit of coffee. In this case, let Brazil sells 12 units of soybeans for 6 units of coffee. Similarly , Peru will sell 1.6 units of coffee for 3.2 units of soybeans. As a result, Brazil will consume 12 units of soybeans and 6 units of coffee whereas, Peru will consume 3.2 units of soybeans and 2.4 units of coffee. Hence, both countries are benefited by trade. The Consumption Possibility Frontier curves thus obtained due to trade are shown in the diagram below. Here, Brazil and Peru shift to new consumption level denoted by points A and B respectively.