international trade econonmics problem

{40 marks) Consider a closed economy, in which an individual's consumer preferences are given by = (2:21 cf)E , where p = 0.5 , there are N firms (i.e. goods varieties) and c, is the quantity of variety 1' consumed. All producers need a fixed labour input of 20 and a variable labour input of 2 per unit of output; there are 600 workers available in the economy. When necessary in the questions below, calculate to two decimal places. Show all working. Page 1 of2 72 i. {6 marks) Show that the demand function for each good, j, is given by cj- = :39} __1, i=1 i. where pl- is the price of variety iand w is the wage. What does this function tell us about how consumer demand varies with income and prices? ii. (4 marks) Given the above consumer preferences, show that the own price elasticity of 1 demand for good} is given by E}- = 2 + 1'); :1 pi1 I iii. {6 marks} Assuming a symmetric equilibrium, show that the profit maximisation (PM) equilibrium condition for this economy is given by% = Kiri11) where w is the wage. iv. (4 marks) Assuming a symmetric equilibrium, show that the zero profit {2P} equilibrium condition for producers in this economy is given by% = $ + 2. v. (10 marks) Using the PM and 2P equilibrium conditions (and one other equilibrium condition), solve for the symmetric equilibrium N, c and %. v1. {10 marks) Imagine that the above economy is suddenly able to trade freely with another identical country. Describe in words what you would expect to happen to (a) prices, (b) production patterns, (c) consumption patterns, (d) trade patterns and (e) welfare in each country