Question

Consider a country, Home, which produces two goods, Cloth and Food, using capital and labour with a constant-return-to-scale technology. Food production is capital-intensive and cloth production is labour-intensive. Capital and labour can move freely between the two industries. Finally, let’s assume that Home’s consumption decisions can be represented using regularly-shaped indifference curves.

1.When Home is not engaged in international trade, use a graphic to illustrate the consumption and production points in Home in autarky (pre-trade situation). (2 points) 2. Assume now that Home has the possibility to trade with another country and the relative price of cloth, PC/PF in the international market, rises. a. What will be the effects of the price change on production and consumption in home? Illustrate your answer. (10 points) b. What will be the trade pattern in Home? Explain and illustrate! (5 points) c. Will there be complete specialization in Home? Why? (5 points) d. Show that Home will gain from trade? Illustrate your answer! (10 points) 3. What will be the impact of the price change on the wage rate and the rental rate of capital in Home? Make sure that you provide the theoretical basis for your answer? (8 points) 4. Would the change in labour endowment affect existing trade pattern in Home? Discuss! (10 points)

Answer 1

1).

Consider the given problem here there are two goods, “C=Cloth” and “F=Food” with “CRS” technology. So, given the situation the “PPF” of the “H=Home” is given by “A1B1” in the fig below. Now the utility function is given by a usual negatively sloped convex to the origin. So, here “E1” be the equilibrium in “autarkic” where “IC” is created a tangency condition with the “PPF”.

Consider the above fig where “E1” be the production as well as the consumption point here, where the “Home” country is consuming “C1” amount of “cloth” and “F1” amount of “Food”.

2).

Now, as we know that the optimum production point will be determined by the “PPF” and the relative price, “Pc/Pf” and the optimum consumption point will be determined by the “Indifference Curve” and “relative price”. So, here initially “P1P1” was the relative price in autarkic situation given in the fig. So, in the autarkic the consumption must be equal to production, => at “E1” “P1P1” create the tangency condition with “PPF” and with “IC”.

Now as the relative price of cloth, “Pc/Pf” increases, => the new relative price is given by, “P2P2”. So, at the new relative price the optimum production point will move right side along the “PPF” and the consumption point will be determined by the tangency point between “IC” and “P2P2”. So, here the “production point” is “Ep” and the consumption point is given by, “Ec”.

Consider the following fig.

So, if we compare these two point we can see that as “Pc/Pf” increases, => the production os “C” will increase and the production of “F” will decreases. The consumption of “C” decreases and the consumption of “F” increases given in the fig.

b).

Let’s assume that “H” be a “Labor abundant” country, => the “PPF” of will biased towards “Cloth”. Now, as the “Pc/Pf” increases, => production point will move right side along the “PPF” to “Ep” and the consumption point will be determined by the tangency point between “IC” and “P2P2” which is “Ec”. So, given the situation “H” is consuming less “Cloths” what they are producing and consuming more “food” compared to what they are producing, => “H” will “export” cloth and will import food.

c).

No, here complete specialization is not possible. As we know that the “PPF” is concave to the origin and the optimum production point will be determined by the tangency condition of “relative price” and “PPF”, because at that point the value of the production will be maximum. So, because the “PPF” is concave the optimum production point does not possible at the complete specialization.

d).

Consider the given fig. where it’s given that initially the equilibrium was “E1”, where the consumption and production points are same and the “Home” country was getting “U1” level of utility. Now, as the relative price increases to “P2P2” the new consumption point is given by, “Ec” and at that point the “H” is getting “U2” level of utility. As we can see that “U2” corresponds higher level of utility compared to “U1”, => implied “Gains form Trade”.