specific factors model

A Specic Factors Model with Price Changes. (30 marks) Let there be two goods, M and F, and three factors of production, Labor (L), capital (K), and land (T). The production function of M is QM: VLMKa and the production function of F is: QF : V LFT: where Q M is the quantity produced of M and Q F is the quantity produced of F. L M and LF are the employment in the M and F sectors, respectively. The total labor endowment is: LM +LF = 41. Workers can freely move between the sectors, while capital and land are spe- cic to the M and F sectors, respectively. Assume the following endowments for capital and land: K=16;T=25; Suppose that there is one representative consumer with the following utility function: U = V DMDF, where U is the utility, D M and DF are the consumption of M and F respec- tively. (a) Assume that in autarky, the price of M is PM = 1. Compute the price of F, PF. (8 marks) (b) Suppose that in the trade equilibrium, PM = 1 and PF 2 1. Compute the optimal consumption bundle of the country. (6 marks) (c) Do workers benet from international trade in this particular case? Compare the utility of workers in trade and autarky to support your answer. (8 marks) (d) Suppose that in the trade equilibrium, the price of M is xed at 1 but the price of F decreases. Will the home country benet from this price change? An intuitive answer will do. (8 marks)