Suppose that the market equilibrium hedonic price function is w(D) = 12 + D2, where D is a continuous non-negative job attribute. Is the job attribute D desirable or undesirable?
Consider 5 workers who care about their consumption and continuous job satisfaction J.
Their preferences are described by the utility function U(C,J) = 2C + J. There are 5 firms that are producing the output using the production function Q(J,L) = L√20−J
1. What are the marginal rate of substitution between consumption and job satisfaction and the marginal rate of transformation between wages and job satisfaction?
2. What are the equilibrium levels of wage and job satisfaction?
3. What is the slope of the wage-job satisfaction locus? Problem 3
Jobs are characterized by wages and continuous layoff risk M (undesirable job attribute). There are 2 firms that are producing the output using different production functions. Firm 1 has a production function Q(J,L) = L√3 + 5M, and firm 2 has a production function Q(J,L) = L√5 + 2M. What is the employer’s offer curve? Draw the offer curve in the wage-layoff risk space.
Suppose the market for discrete job risk consists of multiple heterogeneous workers and multipleheterogeneousfirms. Worker’scompensatedriskpremia Zi aredistributedaccordingto the uniform distribution Zi ∼ U[1,6]. The productivity cost of reducing the job risk for the firm
MCj is distributed according to the uniform distribution MCj ∼ U[2,6].1
1. What is the equilibrium market compensation and the share of risky jobs in this market?
2. Suppose that the government decides to subsidize the cost of reducing job risk, decreasing the cost by s = 2 for all firms. What is the new equilibrium market compensation for the job risk and the share of risky jobs in the economy? Provide the intuition for this change.
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