Eco_370_Hw_Solution

Answers to Homework 2 (30) 1. Continuing from the Question 4 on Homework 1, suppose the following Earned Income Tax Credit (EITC) scheme is put in place. For those whose earned income (i.e. labor income) is less than $100 per week the government gives 20 cents on every dollar earned. For those who earn more than $100 the government gives them $80 per week. Based on the answers to question 4(d) of the first homework, how does this affect the labor supply and earnings of Shelly' Explain your answers. From homework 1, Shelly will work 32 hours. We expect her to be on the flat part of the EITC schedule. This is equivalent to an increase in her non-labor income, V, of $100 per week. So tangency implies ; The budget constraint is C = 320 + 5(168 – L) + 80. So 320 + 5(168 – L) + 80 = 5L – 200 and L = 144(hours), h = 24(hours) > 20(hours), C = $520. Therefore, Shelly would work 24 hours per week and get $520 of total income, i.e. she would work less when there is EITC. Both consumption and leisure increase for her. With the lumpsum subsidy, she would get more consumption with the same leisure; therefore, there is pure income effect; hence she will be less willing to provide labor. (20) 2. Explain why a lump sum government transfer can entice some workers to stop working (and entices no one to start working) while the earned income tax credit can entice some people who otherwise would not work to start working (and entices no one to stop working). A lump sum transfer is associated with an income effect but not a substitution effect, because it doesn’t affect the wage rate. Thus, if leisure is a normal good, a lump sum transfer will likely cause workers to work fewer hours (and certainly not cause them to work more hours) while possibly enticing some workers to exit the labor force all together. On the other hand, the Earned Income Tax Credit raises the effective wage of low-income workers by 40 percent (at least for the poorest workers). Thus, someone who had not been working faces a wage that is 40 percent higher than it otherwise was. This increase may be enough to encourage the person to start working. For example, if a worker’s reservation wage is $10.00 per hour but the only job she can find pays $8.00 per hour, she will not work. Under the earned income tax credit, however, the worker views this same job as paying $11.20 per hour, which exceeds her reservation wage. Furthermore, the EITC cannot encourage a worker to exit the labor force, as the benefits of the EITC are received only by workers. (50) 3. Trans-Fat Corp. is setting up a small Twonky factory in Albany. Table 1 shows the hourly output in Twonkies associated with each level of employment. Table 1 Workers Output 1 5 2 11 3 18 4 26 5 35 6 43 7 50 8 56 9 61 10 65 11 68 12 70 (a) Tabulate and plot the marginal productivity and average productivity of labor curves for the factory. Worker 0 1 2 3 4 5 6 7 8 9 10 11 12 Output Marginal Product 5 6 7 8 9 8 7 6 5 4 3 2 Average Product 5.00 5.50 6.00 6.50 7.00 7.17 7.14 7.00 6.78 6.50 6.18 5.83 5 11 18 26 35 43 50 56 61 65 68 70 (b) If a Twonky retails for $2 each. How many workers would the firm hire if the wage was $12/hr' wage rate = price * marginal product of labor $12 = $2 * MPe MPe = 6 Then, the firm will hire 8 workers. (c) Plot out the short run labor demand curve for the factory for wages between $4 and $20/hr. For the firm’s hiring decision, the relevant points are the ones that lie on the downward sloping portion of the VMPe curve below the point where the VAPe curve intersects the VMPe curve. From part (a), the intersection point is slightly less than 7 workers. Let w* be the wage at the intersection. Then, for any wage that is greater than w*, the short-run labor demand should be zero. (d) What is the elasticity of short-run labor demand for wages close to$12/hr' elasticity of labor demand = percent change in employment / percent change in the wage {(8 - 9 ) / 8} / {(12 – 10) / 12} = -¾ = -.75 (e) Suppose the price of Twonkies increases to $3. How many do they hire now' Since the price of Twonkies increases from $2 to $3, the marginal product of labor will decrease. It means that the firm will hire more workers to produce Twonkies. For example, when the wage is $12/hr, the marginal product of labor is determined as following: $12 = $3 * MPe Therefore, MPe = 4. It means that the firm will hire 10 workers. The firm will hire 2 more workers after the price of Twonkies increased. (f) Suppose instead that the firm is considering expanding the factory so that output at every level of employment is twice as high. How many workers would they hire at $12/hr' Worker 0 1 2 3 4 5 6 7 8 9 10 11 12 By formula, $12 = $2 * MPe MPe = 6 The firm will hire 11 workers. Output Marginal Product 10 12 14 16 18 16 14 12 10 8 6 4 10 22 36 52 70 86 100 112 122 130 136 140