2) Consider a model of workers searching for jobs. Each worker i faces the same distribution of wage F (*) and has a cost of sampling wage offers c. a) [10 points] Derive a condition for how each worker chooses a reservation wage. b) [5 points] Show how the reservation wage depends on the cost of sampling offers c) [15 points] Assume that a firm does not know a potential workers cost of sampling offers but does know the distribution of ci among workers searching for jobs. Show how a profit-maximizing firm will choose an optimal wage offer
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Each worker i will choose a reservation wage, denoted as w_i, such that they will accept any wage offer greater than or equal to their reservation wage, and continue searching for a better offer if the wage offer is lower than their reservation Show more…
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Question 1: Suppose that the markup of goods over wages, μ, is 10% (0.1) and that the wage setting equation is W = P(1-2u + z) where u is the unemployment rate and z is 10% (0.1). a) What is the real wage, as determined by the price setting equation? (5 points) b) Solve for the natural rate of unemployment. (5 points) c) Solve for the natural rate of unemployment if z falls to 5% (0.05) (5 points) d) Show the change from b to c on a wage setting-price setting diagram. (5 points)
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b. Use your answer from part (a) to complete this statement: If workers are paid million available workers and $-$ million workers $-1$ will be hired. c. In 2007 , the federal minimum wage was set at $\$ 5.15$ per hour. Substitute 5.15 for $p$ in the demand model, $p=-0.325 x+5.8,$ and determine the millions of workers employers will hire at this price. d. At a minimum wage of $\$ 5.15$ per hour, use the supply model, $p=0.375 x+3,$ to determine the millions of available workers. Round to one decimal place. e. At a minimum wage of $\$ 5.15$ per hour, use your answers from parts (c) and (d) to determine how many more people are looking for work than employers are willing to hire.
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