International Trade Theory Problem set 5: Monopolistic competition Spring 2015 1. Consider Krugman’s  article on monopolistic competition and international trade. Assume that the consumer’s utility function is given by: U v ( ci ) , i ci where v ( ci ) e . a) Show that for the above specification Krugman’s critical assumption on the derivative of the elasticity of demand with respect to consumption is fulfilled. b) Determine the equilibrium level of consumption, production and the number of goods as a function of L, , . c) Assume that = 1, = 0.5 and consider an exogenous increase in the labor force. Show that the equilibrium levels of consumption (production, number of goods) decreases (increases). 2. An economy has fixed supply of two inputs: unskilled labor (L) and skilled labor (H), and produces two goods: homogenous traditional product (Y) and differentiated modern product (X). Y requires one unit of unskilled labor per unit of output. X requires α units of skilled labor independently of the level of output (fixed setup cost) plus one unit of skilled labor per unit of output (in addition to α). The wage rate of unskilled workers is denoted by w, and the wage of skilled workers by v. Goods are sold at prices pX and pY, respectively (for simplicity you can assume that the price of the traditional good can be normalized to one). Both groups of workers have the same preferences given by the homothetic function: U(CX,CY) = CXαCY1-α, where: CY is consumption of traditional good and CX is an index of consumption of different varieties of modern product. The consumption index is given by: CX N C i i 1 1 where: Ci represents consumption of i-th variety and N the number of available varieties (N is large). i) Describe the equilibrium conditions in the closed economy. Calculate the output levels, prices and the number of varieties. Find the relative wage of skilled versus unskilled workers. Calculate real wages for both groups of workers expressed in terms of both goods. ii) How will the output levels and the number of varieties change when the economy opens up to foreign trade with another, identical country (L* = L, H* = H)? Discuss the volume and the structure of trade. Does this economy gain from trade? Calculate the aggregate utility level in the trading equilibrium and compare it with the autarky equilibrium. iii) Assume now that countries differ in terms of their relative factor endowments. Determine whether trade can lead to factor price equalization between countries.