Q.1 a. For the diagram in part a. put the total allocation of labor on the x-axis and the total quantity of land on the y-axis, and call the origin the cloth-origin. Now, as in an Edgeworth box (if you don't know what this is, look it up) put a di erent origins (the food-origin) above the total allocation of labor and to the side of the total allocation of land, with axes going in opposite directions, so with the quantity of labor axis going from right to left, and the quantity of land axis going from top to bottom.
Draw lines from the origin with slopes indicating share of K relative to L used in production of each good and use this diagram to demonstrate allocation of factors to production of each good. How is this graph di erent yet consistent with the graph you used in HW 6 (if you used the same graph, come up with some di erent graph and comment accordingly)? Undertake part b. from the same question using the same diagram.
b. In the setup for Q.3 a. from HW 6 is it possible for the land to labor utilization ratios in both sectors to be equal to 1=16? What are possible depic- tions of the graphs (as in a. above in this HW) in this case? If this is possible and the case what does this imply about the allocation of resources between the di erent sectors? What will be the relationship between the ratio of cost of labor to cost of land (w=r) relative to industry speci c ratio of utilization of labor to land (L=T) look like in the w=r-by-L=T plane?
c. In the same setup, is it possible for the land to labor utilization ratio to be greater/less than 1=16 in both industries? What if they have the same slope that is greater than/less than 1=16?
Say, for example, the labor to land utilization ratio was 1=4 for food and 1=12 labor to land utilization ratio for cloth. Can we determine the allocation of resources to di erent industries in this case?
d. What implications would the increase in labor (per the above) does this have for a country's specialization in trade if before the population boom they had exactly two countries (the whole world) had the same amount of resources?
Assume substitutability of factors and decreasing marginal productivity of both factors, as well as homogeneous preferences across countries, and identical technologies across countries. Illustrate this idea with a graph.
Q.2 (from Midterm Spring 2010) For this problem, consider the HeckscherOhlin model from our textbook. Let the two goods being produced be ubber,
F, and blubber, B, and let the two factors of production be oil, O, and whales, W. Furthermore, let H be oil abundant, and F be whale abundant, and let ubber be an oil-intensive industry and blubber be a whale-intensive industry.
a. Graph the relationship between the price of ubber, PF , relative to blubber, PB, and the unit cost of oil, o, relative to the unit cost of whale, w. Why is the graph shaped this way?
b. Now graph the relationship between the unit cost of oil relative to the unit cost of whale and the whale-relative-to-oil utilization ratio for both industries. Why are these graphs shaped this way? Is there any di erence in the shape of them? If so, why is there such a di erence?
c. Indicate the e ects of a rise in the relative price of ubber on the graphs, in particular in terms of the unit cost of ubber-to-unit cost of blubber ratio, and the whale-oil utilization ratio. Is there a di erence in magnitude of change in either of the two industries' equilibrium? If so, what accounts for that di erence?
d. Given this setup, what are the general possible patterns of trade (you won't be able to give exact numbers)? Why will these be the possible patterns?
c. What are the net welfare e ects of trade on each country? On each industry (F and B) in each country? On the owners of the factors of
production? What causes these e ects?
d. Discuss some of the main results of statistical tests of the Heckscher-Ohlin model as presented in our text.
Q.3. In the case of `North-South' trade and wage inequality as discussed in our textbook is it possible for a country to have (1) high-skill biased technological progress while (2) redistributing income from high-skill earners to low-skill earners due to opening of new trade? If possible or not possible, illustrate graphically with (1) relationships between relative price of high-skill intensive product to low-skill intensive product and relative high-skill to low-skill wage (in the plane of the same variables) and (2) relative wage of low-skill to high skill labor by relative utilization of low-skilled and high-skilled labor (in the plane of the same variables). If possible explain plausible magnitudes (relative to necessary e ects) of movements in key variables that may generate such dynamics.