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Econ 361 Assignment 2

Problem 1: Minimum Wage (Lecture 11) (14 points)

Suppose the total market demand for labor is given by and the total market supply for labor is given by where w is the hourly wage.

1. What is the equilibrium wage? How many workers are employed in equilibrium? (6 points)

2. Suppose the government imposes a minimum wage of $12. What is the new level of employment? What is the unemployment rate under the minimum wage? (8 points)

Problem 2: Immigration (Lectures 12–13) (21 points)

1. Suppose you are asked to estimate the impact of immigration on the wage of native workers. What are the potential empirical issues associated with estimating the spatial correlation between the fraction of immigrants and the native wage? (5 points)

2. Discuss how the natural experiment of the Mariel Boatlift used by Card (1990) helps mitigate the above issue and identify the causal e↵ect of immigration on wages and employment of native workers. (5 points)

3. It is often seen in the data that when immigrants first arrive, their earnings are below the earnings of natives. However, as they spend more time in the destination country, they begin to earn more than natives. The relationship is often found with cross-sectional data, and is interpreted with assimilation: Immigrants who migrated many years ago have acquired U.S.-specific skills and thereby improved their economic status.

(a) Use 1–2 sentences to describe each of the following 3 types of data: (i) cross-sectional data; (ii) repeated cross-sectional data; (iii) panel data. (6 points)

(b) What is wrong with the assimilation interpretation of the age-earnings profiles of immigrants estimated using cross-sectional data? (5 points)

Problem 3: Compensating Wage Di↵erentials (Lectures 14–15) (35 points)

Suppose there are many types of jobs that o↵er various levels of airborne particulates at the worksite. Workers care about the wage and value a clean working environment, but di↵erent workers value cleanness di↵erently. Firms have to allocate their resources in order to produce a clean working environment, but some firms find it easy (e.g., universities) and some firms find it hard (e.g., coal mines).

1. How is the hedonic wage function determined and what does the slope of the function measure? (9 points)

2. Suppose you have data on a sample of workers, who were randomly drawn from the population. You can observe workers’ characteristics (e.g., gender, age, education, occupation, industry, working hours, wages, etc.). You can also observe the character-istics of their jobs (e.g., whether having flexible working hours or requiring physical strength, etc.) and working conditions, including the level of airborne particulates at the worksite. Suppose you run a OLS regression, where the dependent variable is wage, and independent variables include various characteristics of workers and their jobs. Can you interpret the estimated coefficient on the level of airborne particulates as the slope of the hedonic wage function? Why? (8 points)

Suppose there are 10 workers in the economy, and all workers have the same preferences represented by

where w is the wage and x is the likelihood of being injured in the job. There are only two types of jobs in the economy, a safe job (x = 0) and a risky job (x = 1). Let be the wage paid by safe jobs and be the wage paid by risky jobs. Suppose safe jobs pay $25 per hour (i.e., = 25).

3. What is the wage in risky jobs? What is the compensating wage differential? (6 points)

4. Suppose now that different workers have different preferences, represented by

where worker 1 has d = −5 (i.e., she enjoys the excitement associated with risk); worker 2 has d = −4; worker 3 has d = −3, and so on. Moreover, assume that there are only 3 risky jobs in the economy because of technological reasons. What is the equilibrium wage differential? Can you infer from the equilibrium wage differential that an average worker in the economy is risk aversion, risk neutrality, or risk loving? (12 points)

Problem 4: Discrimination (Lectures 16–17) (30 points)

Is each of the following statement true or false? If your answer is “false,” explain why. (20 points)

1. Suppose black and white workers are perfect substitutes. The equilibrium racial wage gap is determined by the prejudice level of the most prejudiced employers in the labor market.

2. Suppose black and white workers are perfect substitutes. If most firms in the labor market discriminate against blacks, this implies that the wage of blacks must be lower than that of whites.

3. Suppose black and white workers are perfect substitutes. If whites workers dislike working alongside black workers, firms have to compensate white workers for their disutility and therefore sacrifice profits.

4. A result of employers’ use of statistical discrimination against blacks or women is that it will reduce the average wage of blacks or women.

5. Suppose you regress workers’ log wages on an indicator for being female (F) and a vector of observable characteristics (X) including years of schooling. You find a negative and statistically significant estimate of the coefficient on B. This provides a direct and reliable evidence of labor market discrimination against women.

Suppose a firm’s production function is given by

where and are the number of white and black workers employed by the firm, respec-tively. It can be shown that the marginal product of labor is

Suppose the market wage for black workers is $10, the market wage for white workers is $20, and the price of each unit of output is $100. How many workers of each race would a non-discriminating firm hire? How much profit does this firm earn if there are no other cost? (10 points)