A firm wants to hire a worker. The worker can choose two effort levels: "work" or "shirk". The result of the workers effort is an output for the firm, which may take two levels: YL = 50 USD or YH = 100 USD (YL = low output, YH = high output). The actual output depends both workers effort and pure luck. Either level of output can occur if the worker works or shirks, but the lower output is more likely if the worker shirks. Below are the probabilities of the output levels as a function of the workers effort: shirk: probability of output 100 USD = 1/5shirk: probability of output 50 USD = 4/5work: probability of output 50 USD = 1/5work: probability of output 100 USD = 4/5The firm cannot observe the effort, hence it cannot specify the desired effort in the contract. It may only specify the wage as a function of the observed output.The workers expected utility is given by V = h krát odmocnina z (Wh C) + I krát odmocnina z (WI- C), where h, I and Wh and WI denote the probabilities and wages conditional on the high/low output (h = high, I = low). C is the cost of effort: C = 0 if the worker shirks and C = 20 USD if she works. The worker has an outside option which gives him fixed wage 60 USD at zero effort.a) The firm is considering to offer the worker a fixed wage. If the worker accepts the job, what effort will the worker choose? What is the wage that the firm needs to offer such that the worker accepts the job? What is the firms profit? In a table, specify the payoffs and expected utilities for each combination of effort and output, and their expected values.
A firm wants to hire a worker. The worker can choose two effort levels: "work" or "shirk". The result of the workers effort is an output for the firm, which may take two levels: YL = 50 USD or YH = 100 USD (YL = low output, YH = high output). The actual output depends both workers effort and pure luck. Either level of output can occur if the worker works or shirks, but the lower output is more likely if the worker shirks. Below are the probabilities of the output levels as a function of the workers effort: shirk: probability of output 100 USD = 1/5shirk: probability of output 50 USD = 4/5work: probability of output 50 USD = 1/5work: probability of output 100 USD = 4/5The firm cannot observe the effort, hence it cannot specify the desired effort in the contract. It may only specify the wage as a function of the observed output.The workers expected utility is given by V = h krát odmocnina z (Wh C) + I krát odmocnina z (WI- C), where h, I and Wh and WI denote the probabilities and wages conditional on the high/low output (h = high, I = low). C is the cost of effort: C = 0 if the worker shirks and C = 20 USD if she works. The worker has an outside option which gives him fixed wage 60 USD at zero effort.a) The firm is considering to offer the worker a fixed wage. If the worker accepts the job, what effort will the worker choose? What is the wage that the firm needs to offer such that the worker accepts the job? What is the firms profit? In a table, specify the payoffs and expected utilities for each combination of effort and output, and their expected values.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:A firm wants to hire a worker. The worker can choose two effort levels: "work" or "shirk". The result of the workers effort is
an output for the firm, which may take two levels: YL = 50 USD or YH = 100 USD (YL = low output, YH = high output).
The actual output depends both workers effort and pure luck. Either level of output can occur if the worker works or
shirks, but the lower output is more likely if the worker shirks. Below are the probabilities of the output levels as a
function of the workers effort: shirk: probability of output 100 USD = 1/5shirk: probability of output 50 USD = 4/5work:
probability of output 50 USD = 1/5work: probability of output 100 USD = 4/5The firm cannot observe the effort, hence
it cannot specify the desired effort in the contract. It may only specify the wage as a function of the observed output.The
workers expected utility is given by V = h krát odmocnina z (Wh C) + I krát odmocnina z (WI- C), where h, I and Wh
and WI denote the probabilities and wages conditional on the high/low output (h = high, I = low). C is the cost of effort:
C = 0 if the worker shirks and C = 20 USD if she works. The worker has an outside option which gives him fixed wage
60 USD at zero effort.a) The firm is considering to offer the worker a fixed wage. If the worker accepts the job, what
effort will the worker choose? What is the wage that the firm needs to offer such that the worker accepts the job? What is
the firms profit? In a table, specify the payoffs and expected utilities for each combination of effort and output, and their
expected values.
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