Assignment 1, due August 28 (in class) Economic Development August 17, 2020 Material to review before you start: I. To understand how to derive demand functions for goods when the aggregate preferences are CES, read https://cameronharwick.com/blog/howto-derive-a demand-function-from-a-cesmtilityfunction Our case is a bit simpler than that consider in think link - just set ,6\" equal to I. 2. To understand how a monopolist facing a constant elasticity demand curve sets prices, see https://en.wikipedia.org/wiki/Markup_rule. Set'up: Bicycle manufacturing is a monopolistic industry comprised of M rms. The aggregate utility function of a representative consumer is given by U(X0) + Y Where X0 represents all otheer goods and Y is the composite quantity index of bicycles formulated as Y= (yi/5+y/5+---+yi5)- From now on we will treat the U(X0) part as a xed constant and ignore it. Let 1;, denote the portion of the representative consumer's income spent on bicycles. Bicycle manufacturer i's production function is given by yi = A1- - lei where ki denotes the capital employed (at rental rate normalized to I)'. A,- denotes rm-specic productivity parameter. 'For simplicity we assume that capital is the only factor of production needed. I. Show that the demand for bicycles of rm i is of the form ._ 75 1b yi'pi 'E where P = (Elpg'ifl/'l 2. Find each rm's prot maximizing price and show that each rm charges the same markup rate over its unit cost. Also, ShOW that the quantity produced by each rm is increasing function of its productivity 3. The Total Factor Productivity of Revenue for rm i (TFPR.) is dened as pi - yi/ki. Show that at equilibrium each rm must have the same TFPRi. 4. Now suppose that different rms face more or less favorable cost of capital - let the cost of capital for rm i be denoted by 1 + ti where t; > 0 means the rm faces less favorable cost of capital, and converse is true if t,-