help me do question 4 and 5, economics under international trade

4. 2 x 2x2 Heckschm-Ohlin Consider the following Heckscher-Ohlin model. There are two countries in the world, H and F, and two production factors, capital K and labour L. His endowed with Ks = 3f4and L5- : 1,4, and Fis endowed with K; = wand Ly = are. There are two goods, at = 1, 2, preferences over which are given by u(zl,z:3] = 1113111,\". Both countries have accem to the same technologies, which are given by :1 = L1 and :2 = K2. The corresponding unit cost functions are .21 (Lu-,1") = w and Cg(1.tl',1"] = r, where w and r are, respectively, the wage rate and the rental rate. All markets are perfectly competitive. 2 (a) Compute each country's autarky equilibrium. \"'hich variables determine the autarky equilibrium factor- prime? (b) Solve for the world integrated equilibrium. Which variables determine factor prices now? (c) Assume free trade in commodities and no international factor mobility. Under which conditions will this particular model yield factor price equalization? Find the trade equilibrium's patterns of production and trade. (d) Assume now that technologies are of the Cobb-Douglas type with the following unit cost functions: c1(w,1'] = 132331.133 and (:4 (w,1'] = 131,931..sz Factor endowments are as above. Compute the integrated equilibrium. Draw the FPE set. Discuss whether this model still yields factor price equalization. (e) Find the new trade equilibrium's wage-rental ratios. (f) Assume now technologies are dierent across countries for sector 1: 2:\