Question

1. Use the specific-factors model to answer question 1. Assume that there are two industries, agriculture and manufacturing. The agricultural industry uses labor and land as inputs while the manufacturing industry uses labor and capital as inputs. The production function for each good is as follows:

Agriculture Production Function

Land              Labor          Q_A           

20 0                0   

20 1               12        

20 2               22        

20 3              30        

20 4              36        

20 5              40

20 6               42        

Manufacturing Production Function

Capital        Labor             Q_M           

20 0                0

20 1               12        

20 2               22        

20 3              30        

20 4               36        

20 5              40

20 6               42        

a. Assume that the economy has 6 workers. Draw the production possibilities frontier with manufacturing output on the horizontal axis and agricultural output on the vertical axis. Show the values of the horizontal and vertical intercepts and the coordinates of at least two other points of the PPF.

b. Suppose before trade P_M and P_A are equal to one. How much agricultural and manufacturing output should the economy produce? How much revenue would firms make?

c. Draw the price line on the PPF graph that shows the optimum output combination in part b.

d. Suppose that after trade P_M is equal to two and P_A is equal to one. How much of each good should the economy produce?

e. Draw the price line on the PPF graph that shows the optimum output combination in part d.

f. Suppose after trade the consumption of manufacturing goods is equal to 30. What is the quantity of manufacturing exports?

g. What is the quantity of agricultural imports? (Hint: remember that the price of exports times the quantity of exports must equal the price of imports times the quantity of imports).

h. Bonus. What is the consumption of agricultural goods after trade?

Answer 1

Consider the following fig of “PPF” where we have measure the “Manufacturing output” on the horizontal axis and “Agricultural output” on the vertical axis.

So, in the above fig the horizontal intercept is given by, “(M, A) = (42, 0)” and the vertical intercept is given by, “(M, A) = (0, 42)”.

b).Now, assume that “Pa=Pm=1”, => the relative price of “Manufacturing output” is “Pm/Pa=1”. Here the economy should produce such that the value of the total production will be maximum. Consider the above table where “Total_1” shows value of the total production at “Pa=Pm=1”. So, the value is maximum at “M=A=30” mentioned in the above table.

c).Consider above fig here the “RED” downward sloping line be the relative price of the “manufacturing output” and it created the tangency condition at M=A=30. So, the optimum point is “M=A=30”.

d).Now, let’s assume that “Pm=2” and “Pa=1”, => the relative price of “Manufacturing output” is “Pm/Pa=2”. Here the economy should produce such that the value of the total production will be maximum. Consider the above table where “Total_2” shows value of the total production at “Pa=1, Pm=2”. So, the value is maximum at “M=36, A=22” and the corresponding value is “94”, mentioned in the above table.

e).Consider above fig here the “GREEN” downward sloping line be the relative price of the “manufacturing output” when "Pm=2" and "Pa=1", and it created the tangency condition at M=36, A=22. So, the optimum point is “M=36, A=22”.

f).

Suppose that after trade the consumption of “M=30”. We also know that the production of “M=36” at the relative price “Pm/Pa=2”, => the amount of export is “36 – 30 = 6 “.

g).

As we have given the “Pm=2” and “Pa=1” and the given the relative price the country will export “6 units” of manufacturing goods, => M*Pm = 6*2 = 12. So, the agricultural good imported is “M*Pm/Pa = 6*2/1 = 12. So, the “12 units” of agricultural goods will be imported.

h).

Now, at the relative price “Pm/Pa=2” the optimum production of agricultural good is “22” and the country will import “12 units” of the agricultural goods, => the total consumption of “Agricultural good” is “22+12=34”.