Answer the following

4. Vacancy costs and the labor market. Consider the search-theoretic model of the labor market of Diamond {1982), Mortensen (1982} and Pissarides (1985). a. The equilibrium tightness of the labor market, 6", solves the following equation -ny-w luWWW Plot the left and the right hand side of the above equation as functions of 9 and identify 6'. k=so b. Using the same yaph as before, identify the effect of an incraese in the vacancy cost it: on the equilibrium tightness of the labor market. Interpret your nding. c. The equilibrium unemployment, n", and the equilibrium vacancies, v", solve simultaneously the following system of equations Plot the solutions to these two equations in a graph that has it on the horizontal axis and v on the vertical axis (Le. plot the Beveridge curve and the market tightness curve]. Identify n\" and 11*. (1. Using the same graph as before, illustrate the eifect of an increase in the vacancy cost I: on the equilibrium unemployment and vacancies. Interpret your ndings. e. Should the government intervene to lower unemployment in response to an increase in k? In Exercises 9-16, a table is given telling the time needed for each of a number of tasks and which tasks must immediately precede them. Make a PERT diagram for each problem, and determine the project time and critical path. 9. Task Time Preceding Tasks 10. Task Time Preceding Tasks 11. Task Time Preceding Tasks None A None A Non B None B WN U 7 A. B 10 D 2 A, B D 6 A 6 C. D E B. D B. C E B. D C 7 C. D C. E. F 6 D. E. F E. F 12. 13. Task Time Preceding Tasks 14. Task Tine Preceding Tasks Tark Time Preceding Tasks 5 10 None A None None B A. D 12 None 2.1 None C 10 B. I C 15 None None 6 A. C D 7.2 None D None E B 3 A, B E 6.1 None 9 A.B 13 I C F 4.1 G 13 B. C 5 C. E. F H 2.0 F. G 9 None D. E 8.5 D. E. G D. H E, F 5.2 E, H 16. 15. Preceding Tasks Park Time Preceding Tasks Tark Time None A None 13 None A 12 None C .10 A, F B, C 14 None JOT A. C.D E .02 None -IOTMORE E 6 A. B. D 10 A. B. C -11 B. C. D .09 F. G D. H E, F, H 06 F. G. H4. (30 points) Consider the following game. There are ten dollars to divide. Two players are each required to simultaneously name an integer between 0 and 10. The player who names the higher number gets to keep the money. If they name the same number, the money is equally shared between them. (a) Describe the set of players N, the set of strategies { Silien, and the payoff function QuitiEN. (b) Are there strategies that are strictly dominated? Demonstrate your reasoning. What are the resulting strategies after iterated elimination of strictly dominated strategies? (c) Find the best responses (correspondence) for each player. That is, find the strategies that maximize a player's payoff given what the other player does. (d) Find the Nash equilibria of the game. (e) Suppose now the game is changed. Whenever there is a tie, each player receives nothing. Answer the same questions in parts (b) and (c). Find the pure-strategy Nash equilibria of the game.Consider the following annual model of the death rate (per million population) due to coronary heart disease in the U.S. (denoted by Y.): Y, =140+ 10.0C, +4.0E, -1.0M, +e, (2.5) (1.0) (0.5) N = 31 Standard errors are in parentheses where C = per capita cigarette consumption (pounds of tobacco) in year t Et = per capita consumption of edible saturated fats (pounds per butter, margarine) in year t M. = per capita consumption of meat (pounds) in year t a) Do the coefficient estimates in the regression above have the expected sign? I.e. do you expect Bc to be positive, BE to be positive, and By to be negative? Explain. b) Calculate the t-statistic for every coefficient estimate. Assume that the critical t-value for a two- sided test of statistical significance at the 5 percent level is 2.056. Is Ct, Et, or M, statistically significant? c) The most likely cause of a coefficient that is significant in the unexpected direction is omitted variable bias. Which of the variables listed below could possibly be an omitted variable that is causing PM's unexpected sign? (Hint: Use the table below for your answer). Corr (X1,X2) > 0 Corr (X1,X2) 0 Positive bias Negative bias Bomitted