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ECON 151 Spring 2023

Problem Set 1 ANSWERS

Problems based on Ehrenberg, Smith, and Hallock 14e (2021):

Topic

1. Background	1.RQ.8 1.P.2	2 4
2. Overview	2.P.2	5
3. Labor Demand	3.P.6 3.P.8	8 8
4. Labor Demand Elasticities	4.P.2	8
5. Frictions & Monopsony	5.P.5 5.P.6	4 4 . 43

Did you work with other students? List them below:

Please type your name as an affirmation of the Honor Code at the University of California, Berkeley.

“As a member of the UC Berkeley community, I act with honesty, integrity, and respect for others.”

Type your name:

1.RQ.8. [2 points] In discussing ways to reduce lung diseases caused by workplace hazards, one commentator said:

Gas masks are uncomfortable to wear, but economists argue that they are the socially preferred method for reducing the inhalation of toxic substances whenever they can be produced and distributed at less than it costs to alter a ventilation system.

Is this commentator completely foolish, only partially foolish, or not foolish at all? Take a stand and explain, describing what you would need to know about ALL marginal things in order to say something about socially preferred (optimal) methods. [Hint: mention something that rhymes with the phrase “cardinal when I fit” .]

Partially to totally foolish. Definitely some amount of foolish. Socially optimal choices occur when the marginal benefit (“cardinal when I fit” ) equals marginal cost. This odd statement above only mentions costs associated with combating toxic inhalants, and the benefits are also important.

Gas masks are obvious not very fun to wear, and they impede speaking and mobility. You could view these bads either as reductions in marginal benefits or increases in marginal costs. Either way, they need to be part of the calculation. If they were not, then the choice would not be socially optimal. You could describe this with a vignette: if management thinks the costs of gas masks are lower than the costs of fixing the ventilation system, it might go with gas masks, but by doing so it would probably reduce workers’ productivity.

1.P.2. [4 points] Suppose that a least squares regression yields the following estimate:

wi = − 1 + 0. 3 ai (1)

where w is the worker’s hourly wage rate (in dollars) and a is the worker’s age in years. A second regression from another group of workers yields the following estimate:

wi = 3 + 0. 3 ai − 0. 01 ai2 (2)

(a) [1 point] How much is a twenty-year-old predicted to earn according to the first estimate using equation (1)? Show your work.

When a = 20, the first equation predicts w = – 1 + 0.3 * 20 = – 1 + 6 = 5 ⇒ w = 5

(b) [1 point] How much is a twenty-year-old predicted to earn according to the second

estimate using equation (2)? Show your work.

When a = 20, the second equation predicts w = 3 + 0.3 * 20 – 0.01 * 202 = 3 + 6 – 0.01 * 400

= 9 – 4 ⇒ w = 5

Gadzooks!! The same!

(c) [1 point] In equation (2), the wage function is a quadratic in age. Which way does the parabola open, up or down? Briefly explain why.

The parabola opens downward because the coefficient on age-squared is negative. As age increases, that term dominates. (You could also be all mathy and say that the second derivative is negative.)

(d) [1 point] In equation (2), the wage function is a quadratic in age. At what age is the wage maximized or minimized? Does this seem realistic? Briefly discuss.

You could answer this in a variety of ways. The easiest is to invoke the formula for

y = a x2 + b x + c, where the vertex occurs at – b/2a. That happens to be true because that’s where the derivative is zero. Thus with b = 0.3 and a = –0.01, we are looking at a* = 15 which is not very realistic at all, unless we are talking about a job playing video games or something.

2.P.2. [5 points total] Suppose that supply and demand for school teachers are given by

LS = 20,000 + 350 W

LD = 100,000 – 150 W

where L = the number of teachers and W = the daily wage.

(a) [1 point] Solve for the equilibrium wage and employment levels in this market. Show or describe your work.

We could invert these functions first and set the wages equal, solving for labor, or we can just proceed by setting the labor quantities equal and solving for the wage.