Consider the following variation on the one-sided search model. . Two time periods. No discounting (i.e....

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Consider the following variation on the one-sided search model. . Two time periods. No discounting (i.e. the interest rate r equals 0). • In each period, an unemployed worker gets a job offer with probability 1. • Job offers consist of two elements: a wage w and the effort level e which the worker is required to exert. Assume that effort is perfectly observable, such that the worker always exerts the required effort. • Half of all jobs offer w = 20 and e = 5, while the other half offer w=12 and e = 1. • If a worker earns w and has to exert effort e in a certain period, his utility in that period equals wae, where 0 < a < 2 is a coefficient which indicates how much the worker dislikes effort. • A worker who is unemployed at the end of a certain period receives unemployment benefits b = 9. • Jobs last until the end of time (i.e. there is no job destruction). Answer now the following questions. H. (6 points) Derive an expression for Ve(w, e), i.e. the present discounted value of ac- cepting a wage offer (w, e) in the first period. I. (6 points) Show that a worker who is unemployed at the beginning of the second period will accept either job offer. J. (6 points) Using your answer to the previous question, show that Vu, i.e. the present discounted value of rejecting a job offer in the first period, equals 25 - 30. K. (6 points) For what values of a will workers reject the wage offer with w = 12 and e = 1 in the first period? Present your answer as an inequality, e.g. a < 1. Consider the following variation on the one-sided search model. . Two time periods. No discounting (i.e. the interest rate r equals 0). • In each period, an unemployed worker gets a job offer with probability 1. • Job offers consist of two elements: a wage w and the effort level e which the worker is required to exert. Assume that effort is perfectly observable, such that the worker always exerts the required effort. • Half of all jobs offer w = 20 and e = 5, while the other half offer w=12 and e = 1. • If a worker earns w and has to exert effort e in a certain period, his utility in that period equals wae, where 0 < a < 2 is a coefficient which indicates how much the worker dislikes effort. • A worker who is unemployed at the end of a certain period receives unemployment benefits b = 9. • Jobs last until the end of time (i.e. there is no job destruction). Answer now the following questions. H. (6 points) Derive an expression for Ve(w, e), i.e. the present discounted value of ac- cepting a wage offer (w, e) in the first period. I. (6 points) Show that a worker who is unemployed at the beginning of the second period will accept either job offer. J. (6 points) Using your answer to the previous question, show that Vu, i.e. the present discounted value of rejecting a job offer in the first period, equals 25 - 30. K. (6 points) For what values of a will workers reject the wage offer with w = 12 and e = 1 in the first period? Present your answer as an inequality, e.g. a < 1.

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hIntertemporal budget constraint depicts that the sum of consumption in both periods must be equal t... View the full answer