Economic growth and economic development 584

Introduction to Modern Economic Growth Denote the prices of these two firms by p1 and p2 Show that the price difference that would make the consumer indifferent between purchasing from the two firms satisfies p1 − p2 = (2x − z1 − z2 ) t with t (z1 − x) + p1 ≤ R (2) Suppose that p1 and p2 satisfy the above inequality Then show that all x0 ∈ [z2 , x) strictly prefer to buy from firm and all x0 ∈ (x, z1 ] strictly prefer to buy from firm (3) Now assume that there are three firms along the circle at locations z1 > z2 > z3 Show that firm 2’s profits are given by ả p1 p2 z1 z2 p3 − p2 z2 − z3 π2 (p1 , p2 , p3 | z1 , z2 , z3 ) = (p2 − ψ) + + + 2t 2t and calculate its profit maximizing price (4) Now look at the location choice of firm Suppose that p1 = p3 Show that it would like to locate half way between z1 and z3 (5) Prove that in a symmetric equilibrium with N firms, the distance between any two firms will be 1/N (6) Show that the symmetric equilibrium price with N equity-distant firms is t p=ψ+ N (7) Explain why the markup here is a decreasing function of the number of firms, whereas it was independent of the number of firms in the DixitStiglitz model 570