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Problem 7 (Signaling) Consider Spence's signalling model. A worker's type is t c (0, 1). The probability that any worker is of type t = 1 is equal to 2/3. while the probability that t = 0 is equal to 1/3. The productivity of a worker in a job is (t + 1)'. Each worker chooses a level of education e 2 0. The total cost of obtaining education level e is C(elt) = e' (2 - t). The worker's wage is equal to his expected productivity. 1. Find pooling equilibrium education levels. 2. Find separating equilibrium education levels. Problem 8 (Moral Hazard) Consider the Principal-Agent model discussed in the slides. Suppose that the effort exerted by the agent can take one of three values ec {1/3,2/3). Also suppose that the Agent's preferences are given by u(w, e) = 2w/2 -e. Leisure yields to the Agent a reservation utility y = 1. The principal's problem can have one of two outcomes: success or failure {7,q}. The payoffs to the Principal in these two events are: 7 = 4 if the outcome is a success and q = 0 if the outcome is a failure. The probability of a success is: pig = 1/3 if the Agent chooses the low effort; and py = 2/3 if the agent chooses the high effort. 1. Let effort be observable. Compute the full-information wages at each effort level. What is the profit maximizing effort for the Principal? 2. Now suppose that the Principal cannot observe effort. For each effort level find output dependent wages that induce the Agent to exert such an effort. 3. Which effort level maximizes the profits of the principal if he cannot observe effort? Which wage schedule should he set to induce the agent to exert such effort.The Geller Company has projected the following quarterly sales amounts for the coming yean Q1 02 03 04 Sales $270 $330 $390 $540 F a. Accounts receivable at the beginning of the year are $420. The company has a 45- day collection period. Calculate cash collections in each of the four quarters by completing the following: (Do not round intermediate calculations and round your answers to the nearest whole number, e.g.. 32.) Beginning receivables _2--_ Sales Cash GOIIBCtiOI'lS Ending receivables b. Accounts receivable at the beginning of the year are $420. The company has a 60- day collection period. Calculate cash collections in each of the four quarters by completing the following: (Do not round intermediate calculations and round your answers to the nearest whole number, e.g., 32.) What does the following Tukey post hoc test output tell you about this study (Note: refer to the descriptive statistics for means)? Multiple Comparisons Dependent Variable: Time (1) Course (J) Course 95% Confidence Interval Mean Lower Upper Difference Std. Error Sig. Bound Bound (IJ) Intermediate 3.60000* 1.43088 -046 .0523 7.1477 Beginner Advanced 3.80000* 1.43088 .034 .2523 7.3477 Beginner -3.60000* 1.43088 .046 -7.1477 -0523 Turkey Intermediate HSD Advanced .20000 1.43088 .989 -3.3477 3.7477 Beginner -3.80000* 1.43088 .034 -7.3477 -.2523 Advanced Intermediate -20000 1.43088 .989 -3.7477 3.3477 That workers in the beginner condition solved the problem significantly faster than workers in both the advanced and intermediate condition That workers in the beginner condition solved the problem significantly slower than workers in both the advanced and intermediate conditionSuppose Jan chooses Bundle d when faced with budget line L- and Bundle e when faced 12 with budget line L Given Jan's revealed preferences, draw an indifference curve for her through Bundle a using the three-point curved line drawing tool (1). Attach the provided label. d a Y, Units per week e X, Units per weekThe Geller Company has projected the following quarterly sales amounts for the coming yean 01 02 Q3? 04 Sales $270 $330 $390 $540 ' 8. Accounts receivable at the beginning of the year are $420. The company has a 45 day collection period. Calculate cash collections in each of the four quarters by completing the following: (Do not round intermediate calculations and round your answers to the nearest whole number, e.g., 32.) Beginning receivables _2_ __ Sales Cash DOilBCtIOI'IS Ending receivables b. Accounts receivable at the beginning of the year are $420. The company has a 60 day collection period. Calculate cash collections in each of the four quarters by completing the following: (Do not round intermediate calculations and round your answers to the nearest whole number, e.g., 32.)