Specificc factor model

3 Specic factor model: 30 points In this economy two countries, Home and Foreign, produce two goods, Com- puters and Desks, using three factors of production, skilled labor (H), un- skilled 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 = H1'2K5'2 (1) their income is given by the prots RC = PCQC 'rKC Unskilled workers are also self-employed. They rent capital and use it to produce desks according to the production function: Q9 = 1,me (2) their income is given by the prots R9 = PD * Q D TX}; 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. Remember that in the economy all the factors are always fully employed. Assume for now that the two countries are in autarky. 1. (6 points) Derive the production possibility frontier for both countries using the 4-quadrant graph seen in class. 2. (8 points) Suppose the price of desk relative to that of Computer is 3. Consider the Home country and nd the autarky equilibrium return to capital am using the graph showing the Value Marginal Product of Capital p x M PK for both goods. What is the allocation of Capital to the production of the two goods? Determine the output of computers and desks