There is a typo in the question that says use rg for Gold, when in fact it meant use rd for Diamonds, because gold is not a factor in this problem

Q1 Specic Factors Model Consider the following small open economy (who takes world prices as exogenous). There are two goods produced: cabinets (C) and jewelry (J). Producing cabinets requires trees (T) and labour (L) Producing jewelry requires diamonds (D) and labour (L) Note that trees are specic to cabinet industry, while diamonds are specic to the jewelry industry. Labour can move between the cabinet and jewelry industry. The production technology for cabinets is: Qc = TlfaL'a Where T is measured in numbers of trees, and L is measured in numbers of people. The production technology for jewelry is given by: Q; = .DzaLy3 Where D measured in kilograms. The economy is endowed with 8 kilograms of diamonds, and 512 trees. 110 individuals live in this economy, each of whom is willing to supply their labour for any wage. The nominal world price of a unit of jewelry is p; = 6 while the world price of a cabinet is pg = 1.5. In what follows, denote the price of a unit of labour by w, the price of a tree by n and the price of a. pound of gold by rg. Assume that both input and output markets are perfectly competitive. a) Solve for the demand for labour in the cabinet industry and the jewelry in- dustry. b) What is the equilibrium allocation of labour across industries? What is the equilibrium wage? Draw a picture showing this equilibrium. c) What is the real return to labour in terms of cabinets? What is the real return of trees in terms of jewelry