3. Local prices and gentrification. Using the search-theoretic model of price dispersion of Burdett and Judd (1983), we want to understand the effect of gentrification on local prices. Consider a neighborhood populated by a measure 1 of local buyers and a measure 1 of sellers. Each local buyer wants a unit of some good, which gives him a utility of u > 0. Each seller has the technology to produce the good at the unit cost ce (0, u). Buyers can only shop from a small number of sellers on a given day. Specifically, a buyer can shop from 1 randomly-selected seller with probability oz,1 = AE (0, 1) and from 2 randomly-selected sellers with probability or,2 - 1 - 1. a. Write down the equilibrium distribution of posted prices F(p). What is the key property of F? b. Write down the equilibrium distribution of transaction prices G(p). Explain the formula. c. What is the sign of the difference between F and G? Explain. Now, suppose that a fraction 1/2 of the local buyers are displaced by newcomers. Each newcomer can shop from 1 randomly-selected seller with probability ox,1 - / and from 2 randomly-selected sellers with probability 0N,2 - 1 - 4. Newcomers are busy relative to locals, in the sense that a > A. d. After the displacement of locals, what is the fraction a1 - a of buyers who can shop from only one seller? What is the fraction 62 - 1 - a of buyers who can shop from multiple sellers? Compare a to A. e. After the displacement of locals, what is the equilibrium distribution of posted prices F(p)? And the distribution of transaction prices G(p)? f. What happens to posted prices because of the displacement of locals? [Hint: compute the difference between F and F] Explain. g. Do locals pay more or less after the arrival of the newcomers? Explain