We solve the 2 x 2 Ricardian model with a constant elasticity of substitution (CES) demand. Assume that the demand in country n of the goods i, yni, is the result of the utility maximiza- tion: max x [(Uml) + (Un2)²=11 s.t. Pnlnl + Pn2Yn2= Xn, where n = N, S indexes the country, and X, is the total expenditure of the country. σ > 1 denotes the elasticity of substitution across goods. (a) Write down the Lagrangian function and solve for the optimal consumption bundle for country n. (b) The ideal price index is defined as the cost of one unit of utility. Show that with CES utility function, the price index takes the form: Pn = [(Pm1) + (P2)¹- (c) Under the assumption of free trade, law of one price holds so we have PN₁ = Ps₁ = P1; and psi = Ps2 = p2. Solve for the world relative demand of the two goods. (d) Same as in the lecture, we assume the North has comparative advantage in goods 1, so: aN2 asi as2 Derive the world relative supply of the two goods. (e) Derive the autarky real wage in the North. (f) Derive the real wage in the North under trade, and compute its gains from trade.

We solve the 2 x 2 Ricardian model with a constant elasticity of substitution (CES) demand. Assume that the demand in country n of the goods i, yni, is the result of the utility maximiza- tion: max x [(Uml) + (Un2)²=11 s.t. Pnlnl + Pn2Yn2= Xn, where n = N, S indexes the country, and X, is the total expenditure of the country. σ > 1 denotes the elasticity of substitution across goods. (a) Write down the Lagrangian function and solve for the optimal consumption bundle for country n. (b) The ideal price index is defined as the cost of one unit of utility. Show that with CES utility function, the price index takes the form: Pn = [(Pm1) + (P2)¹- (c) Under the assumption of free trade, law of one price holds so we have PN₁ = Ps₁ = P1; and psi = Ps2 = p2. Solve for the world relative demand of the two goods. (d) Same as in the lecture, we assume the North has comparative advantage in goods 1, so: aN2 asi as2 Derive the world relative supply of the two goods. (e) Derive the autarky real wage in the North. (f) Derive the real wage in the North under trade, and compute its gains from trade.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter4: Estimating Demand

Section: Chapter Questions

Problem 6E

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