Question

[Specific factor model] Assume that there are two goods: cloth (C) and food (F). There are 3 factors: labor (L), capital (K), and land (T). ) What is the slope of the production possibility frontier? 2) Graph the wage rate and the allocation of labor between the two sectors. 3) Determine the output of each sector using PPF. 4) Graphically show that the change in relative prices leads to the change in allocation of labor and output combination. And determine the relationship between the relative prices and the relative quantities supplied. 5) Explain the pattern of trade in the specific factor model with graphs. 6) Who gains and who loses from the international trade in the specific factor model? 7) Explain why international trade is beneficial to the whole country with graphs in the specific factor model.

Answer 1

Consider the given problem there are two goods “C=Cloth” and “F=Food” and there are three factor production labor(L), capital(K) and land(T). So, given the technology the PPF of this economy is given below.

So, here we have measures “F” on the horizontal axis and “C” on the vertical axis and AA’ be the PPF of the economy which is concave to the origin.

2).

So, there are two goods, “F” and “C”, => the demand for labor in “F” is given by, “WF = PF*MPLF”. Similarly, the demand for labor in “C” is given by, “WC = PC*MPLC”. Now, as the “MPL” is downward sloping the demand for labor in both the sector is also negatively sloped. Now, if “WF > WC”, => all the labor will shift towards “F” industry and if “WF < WC”, => all the labor will shift towards “C” industry. So, in the equilibrium the wage rate in both the sector must be same. Consider the following fig.

So, here we have measured “F” on the right side and “C” on the left side, “VMPLC” be the demand for labor for “C” and “VMPLF” be the demand for labor for “F”. Now, “E” be the equilibrium here, and “L*F” of the labor goes to “F” and “L*C” labor goes to “C” and the equilibrium wage is “W*C=W*F” in the economy.

c).

Now, let’s assume that “PF” be the price of “F” and “PC” be the price of “C”, => given these price the relative price of “F” is given by, “p=PF/PC”, => the optimum production point will be the determined by the condition MRT=p, => in the above fig. PP’ be the relative price and AA’ be the PPF, => the optimum production point is “E0”. So, the optimum production of “F” and “C” are “F*1” and “C*1” respectively.

d).

So, the labor demand for food is “WF = PF*MPLF”, now if the “PF” increases given “PC” same, => relative price of “F” increases and as “PF” increases, => the demand for “F” increases, => “VMPLF” will shift to “VMPL2”, => the new equilibrium is given by “E1”, => LF will increases and “LC” decreases, => the production of “F” also increases as more labor goes to “F” industry on the other hand the production of “C” will decreases. Consider the following fig.

5).

Now, if “F” is land intensive good and the country “Land” is abundant factor, => the autarkic relative price of “F” of this country should be lower compared to other country, => given this situation this country will export “F” which uses abundant factor of this country and will import “C” for other country which abundant in “capital”.