# Given the production functions, write down the PPF for the Home country using the idea that capital is employed in both sectors.

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: QC = H1/2K 1/2 C (1) Their income is given by RC = PCQC – rKC, where KC 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: QD = L 1/2K 1/2 D (2) Their income is given by RD = PDQD – rKD, where KC 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) = X 1/3 C X 2/3 D . (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 specific 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 QD as the horizontal axis and QC as the vertical axis.