Question

Suppose jobs vary along two dimensions: wages and noise and that all workers dislike noise but vary in their distaste for it. Assume that the combinations of wages and noise for which firms’ profits are zero are given by the equation W = 5 + .1N (for 0?N?100) where W is the wage in dollars per hour and N is the noise the worker is subjected to, in decibels. Also, assume at the jobsite of any firm that spends nothing on noise reduction N = 100. a. Draw the offer curve. b. Assume two employed workers, Manny and Moe. Assume that at Moe’s jobsite workers are subject to 50 decibels of noise and at Manny’s workers are subject to 75 decibels. Draw one indifference curve for Manny and another for Moe, representing their respective utilities at their respective jobs. What are these workers’ wages? c. Which worker has a greater willingness to pay for a one decibel reduction in noise at the wage-decibel combination of $10 and 50 decibels? d. At their current wages and levels of noise, how much wage is Manny willing to give up to reduce noise by one decibel? How much wage is Moe willing to give up to reduce noise by one decibel? e. Suppose OSHA sets a cap of 50 decibels at all jobsites. How does this cap affect Manny’s and Moe’s employment choices? How does the cap affect Manny’s and Moe’s well-being? f. Assume again no OSHA and no cap. Suppose it becomes costless for firms to reduce or eliminate noise. What does the new offer curve look
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like? What would be the new combinations of wage and noise chosen by Manny and Moe? Are they better off at these new combinations of wage and noise? Are their employers better off?

Answer 1

JOBS AND NOISE

A. In order to graph de supply curve you must understand the supply function. W = 5 + 0.1N This information tell us that the supply curve intercepts the y axis at 5, is upward sloping and has a slope of +0.1. . When graphing wages generally wage is in the Y-axis and the other variable in the x-axis. Remember: in order to graph any curve you need al least 2 points.

We can find the first point by calculating what the wage offer of the company when the firm does not spend in noise reduction (N=100) just substitute this value in the supply function,

W = 5 + 0.1N = 5 +0.1(100) = 15

W=15

First point in the graph (100, 15)

Second point: you can pick any value of N between 0>N>100. In this case I used N= 50

W = 5+ 0.1(50) = 10

W= 10

Second point: (50, 10)

Third point: thanks to the function, you already know that the interception in the y-axis is at 5. Therefore this point is equal to (0,5) This also means that if the company spends all the money in noise reduction, the wage will be 5.

  Your supply curve should look like this:

B.

In this question, you only have the information of two workers (Manny and Moe) and their current noise levels in their respective jobs. If they are actually working, this means that MUL/MUc=w, in other words, this means that at this wage, the budget line is equal to the indifference curve.

In order to obtain these points, you just need to substitute the values of N for Manny and Moe in the function.

Moe N=50

W = 5+ 0.1(50) = 10

Moe’s wage = 10

Manny

W = 5 +0.1(75) =12

Manny’s wage = 12

Your graph should look like the next one, where Moe's utitity= 10 (total wage) and Manny's utility =12

c. For this question you can compare the elasticity of Moe and Manny, and the current wage ratio.

To obtain this, because we need the elasticity of one point, you just need to divide X/Y= N/w

Current wage: 50/10 =5

Moe’s elasticity: 50/10 =5

5 = 5 Therefore, Moe is getting what he wants so he will not be willing to spend more on noise reduction

Manny’s elasticity = 75/12 = 6.25

5 < 6.25 Therefore Manny will be the one willing to spend more money.