Two countries, Home and Foreign, produce two goods, Computers and Desks, using three factors of production,
skilled labor (H), unskilled labor (L) and capital (K). Skilled workers are self-employed. They rent capital at the rental rate r and produce computers according to the production function: QC = H 1 2 K 1 2 C , their income is given by the profits RC = PCQC−rKC. Unskilled workers are also self-employed. They rent capital and use it to produce desks according to the production function: QD = L 1 2 K 1 2 D their income is given by the profits RD = PDQD − rKD. The Home country is endowed with the following factor amounts:H = 9, K = 20, L = 4. The Foreign country is endowed with the following factors: H∗ = 1, K∗ = 20, L∗ = 4. Preferences are identical in the two countries and are described by the following utility function: U(CC, CD) = C 1 3 C C 2 3 D Remember that in the economy all the factors are always fully employed. Assume for now that the two countries are in autarky. 1. Derive the production possibility frontier for both countries using the 4-quadrant graph seen in class. [5pt] 2 2. Given prices of Computers and Desks, pC and pD, consider the Home country and find the autarky equilibrium return to capital rK using the graph showing the Value Marginal Product of Capital (p×MPK) for both goods. What is the allocation of Capital to the production of the two goods?  3. Now consider the Foreign country and, for given prices p ∗ C and p ∗ D find the return to capital r ∗ K using the same method as in part 2. What is the allocation of Capital to the production of the two goods?  4. Take the Home country and consider an increase in the relative price pC. What is the effect of this price change on the income of the skilled (RH) and unskilled workers (RL).  5. From parts 2 and 3 you are able to derive the relative supply of the two goods in both countries. Knowing preferences you can also derive the relative demand for each country. Using relative demand and relative supply find for each country the equilibrium autarky relative price: pC pD A and pC pD A∗ . You should use Desk as the numeraire good by setting its price to one.  6. Now imagine the two countries can trade. Derive the world relative supply curve and find the equilibrium world relative price.
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