1. (55) Declining Search Frictions and the Beveridge Curve. Using the searchtheoretic model of unemployment and vacancies of Pissarides (1985), we want to understand the effect of declining search frictions. To this aim, assume that the matching function M (u, v) has the form A-M(u, 1)), where A > 0 is a parameter that controls the efciency of the matching process (i.e., a parameter that is inversely related to search frictions) and M(u,o) is a constant returns to scale function that is increasing and concave in both a and 1). a. (5) For 5 = 1, the equilibrium tightness of the labor market, 6*, solves the following equation k = Aqwxl 13%. where 16(9) E M (1, 6') and 6(9) E M (61, 1). The lefthand side is the rm's cost of opening a vacancy. The right-hand side is the rm's benet of opening a vacancy. Plot the left and the right hand side of the above equation as functions of 0 and identify 6*. b. (5) Using the equilibrium condition for 9* identify and explain the two opposing effects of an increase in the efciency A of the matching process on the rm's benet of opening a vacancy. c. (10) Differentiate the rm's benet of opening a vacancy with respect to A, and identify the dominant effect. (1. (5) Using the same graph as in (a) and the result in (c), identify the effect of an increase in A on the equilibrium tightness of the labor market. . e. (5) The equilibrium unemployment, u*, and the equilibrium vacancies, v*, solve simultaneously the following system of equations 8 + Ap(v/u)' v = 0*u. Plot the solutions to these two equations in a graph that has u on the horizontal axis and v on the vertical axis (i.e. plot the Beveridge Curve and the vacancy creation curve). Identify u* and *. 2 f. (10) Using the same graph as in (e), illustrate the effect of an increase in A on the Beveridge Curve. Interpret your findings. g. (5) Using the same graph as in (f) and the result in (d), illustrate the effect of an increase in A on u* and v* . Interpret your findings.h. (5) Below you see the Beveridge curve for the US, and the time-series of unemployment and vacancies. Can you think of reasons why techological progress that has ostensibly improved the efficiency of the matching process has not resulted in a progressive shift of the Beveridge curve and a downward trend in unemployment? + 1927-1936 3 1937-1946 25 -v 8 1947-1956 7 1957-1966 7 1967-1976 20 6 1977-1986 6 x 1987-1996 194 O 1997-2006 5 Vacancy Rate 2007-2018 15 Vacancy Rate Unemployment Rate + 3 3 2 5 O 5 10 15 20 25 30 1930 1940 1950 1960 1970 1980 1990 2000 2010 Unemployment Rate Time i. (5) Relating back to Question 1, can you think of reasons why technological progress that has improved the efficiency of monitoring has not resulted in a downward trend in unemployment