I have some questions on how to solve these problems.

1. (Specic Factors Model: Autarky Economy) In this economy 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). Technology. Technology is the same in both the Home and Foreign countries. In both countries, skilled workers are self-employed. They rent capital at the rental rate r and produce computers according to the production function: Qo = HI/QK\" (1) Their income is given by RC : PCQC TKO, where K0 is the capital employed to produce computers. Unskilled workers are also self-employed. They rent capital and use it to produce desks according to the production function: Q9 2 le2gg2 (2) Their income is given by RD : PDQD TKD, where K0 is the capital employed to produce computers. [NOTE: I updated the production function for desk, so that you will have a beautiful \"closed-form\" solution to capital rental rate in (c)] Endowments. 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. Preference. Preferences are identical in the two countries and are described by the following utility function: U(XC,XD) : xg3xg/3. (3) In the economy all the factors are always fully employed. Assume for now that the two countries are in autarky. (a) In this model, what are the specic factors to produce each product? (b) Given the production functions, write down the PPF for the Home country using the idea that capital is employed in both sectors. Plot it on a graph with QB as the horizontal axis and QC as the vertical axis. (c) Suppose prices of Computers and Desks, PC and PD. Consider the Home country and nd the autarky equilibrium return to capital '3" using the graph showing the Value of Marginal Product of Capital P a: M PK for both goods, following the steps: i. Draw the capital demand for these two industries in one graph. (Hint: capital demand in each industry is determined by P a: M PK : 3".) ii. What is equilibrium capital rental rate r and the allocation of Capital to the production of the two goods (as a function of PC and PD)? iii. What are the corresponding outputs of each product (as a function of PC and P3)? In particular, what is the relative supply function Qc/QD as a function of Par/PD? ((1) Suppose the output prices are PC and PD, and given that the capital rental rate r is a function of PC and PD, solve for the demand for computers and desks by solving the consumer utility maximization problem for skilled workers and unskilled workers at Home country. In particular, what is the relative demand function Xc/XD as a function of Par/PD? (e) Using relative demand and relative supply, nd the equilibrium autarky relative price for the Home country. Draw the relative supply and relative demand function for Home in one gure and mark the equilibrium point as A. [NOTE because you can only nd the relative price PC/PD, you could use Desk as the numeraire good by setting its price PD to one.] 2. (Specic Factors Model: trade) In the above question, now suppose the two countries are allowed to trade with each other freely. (a) Find the world relative supply flmction. [Hint: solve for the foreign supply function as you did for Home. Combine Home and Foreign to get the result.] (b) What is the world relative demand function? (c) Draw the relative supply and relative demand function for the world in one gure, and nd the equilibrium world relative prices Pow/PD. Mark the world equilibrium point as B. i. Is it higher or lower than the Autarky equilibrium relative price at Home? ii. Compare it with the Autarky equilibrium point A as you nd in Question 3 (e), show which factors gain and which lose from allowing free trade between the two countries. ((1) What is the effect of this change in relative price on the income of the skilled (RS) and unskilled workers (RU)