The question is attached as follow:
1. [Specific Factors Model: Antarky 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: so = Bragg: (1) Their income is given by RC = Pch: TKC, where K3 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: Q3 = wing\" (2} Their income is given by Rn = PoQo rKn, 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 foilowing 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,Xp] X,','3xf,'3. (3} In the economy all the factors are always fully employed. Assume for now that the two countries are in autarky. In this model, what are the specic factors to produce each product? 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 C29 as the horizontal axis and QC as the vertical axis. Suppose prices of Computers and Desks, PC: and PD. Consider the Home country and nd the autarky equilibrium return to capital 1' using the graph showing the Value of Marginal Product of Capital P =1: MPK for both goods, following the steps: i. Draw the capital demand for these two mdustries in one graph. (Hint: capital demand' In each industry' is determined by P * MPK = r } 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 PD)? In particular, what is the relative supply function chQg as a function of chPD? Suppose the output prices are Po and PD, and given that the capital rental rate r is a function of Pa and Pp, 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 chXp as a function of Pc/Pp? 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 figure and mark the equilibrium point as A. [NOTE because you can only nd the relative price Pc/Pp, you could use Desk as the numeraire good by setting its price Pp to one]
