Labor Market, Wages and Unemployment Problems 3, 5 & 7

Chapter Seven Review Questions

Question 3 – Positive Oil Shock – Suppose scientists discover a new way to extract oil from deposits that were previously thought to be unrecoverable. The extra supply of oil leads oil pries to decline by $5 per barrel. Explain the effect on wages, the employment-population ratio, and unemployment – all for the overall economy. 

See pages 172 – 173. Be prepared to draw the nice diagrams (Figures 7.3 to 7.6) and discuss the economic intuition of how firm’s would react to a change in business conditions – how this would affect the labor market.

Exam time; you might be asked about things that affect the labor supply curve like tax rate (tau). Be sure to differentiate this from changes that would affect labor demand (page 172, figure 7.3), and how a minimum wage works and what it looks like (figure 7.6)

The price of oil affects most firm’s production costs both directly (if they use oil as an input) and indirectly (in oil price’s effect on energy and transport costs). A decrease in cost of oil will therefore likely increase the demand for labor – a right-ward/upward/outward shift in the labor demand curve. This increases the wage rate, increases the employment-population ratio and decreases unemployment.

More intuitively, with the price of oil decreasing (and expected prices permanently lower), the marginal product of labor (MPL) increases and firms will seek to hire more labor. In order to induce workers in other jobs and those currently not working, these higher MPL firms must increase the wage. As non-working people are induced into the labor market by the higher wages the unemployment rate will decrease and the employment-population ratio will increase.

Question 5 – Present discounted values (II) – Repeat exercise 4 (answer on page 187+) for an interest rate of 1% then for an interest rate of 5%. Arrange your answers in a table so you can more easily see the difference a change in the interest rate makes. 

 See pages 178 – 181 and churn it out. Help also lies in page 187. 

Although you won’t have a calculator on the exam, you’d want to show that you could calculate all this if you had to (page 187 for step by step help). An exam also might give you a simple enough problem that your pre-calc skills should allow you to work toward a solution.

Examples of calculations.

(a) $50,000 in one year with an interest rate of 1%. 

Where is the present discounted value of the object today,  is the interest rate.  is the number of periods, 

Repeat for 3% & 5%

(b) $50,000 in ten years at 1%. 

(c) $100 each year forever at 1%.

(d) $100 each year for fifty years at 1%.

Question 7 – Valuing human capital with wage growth – To make the calculation of the present discounted value of a worker’s human capital more realistic, supplose labor income starts at $50,000 initially, but then grows at a constant rate of 2% per year after that. 

See pages 178 – 181 and churn it out & be ready to show your work.

The Formula for the Geometric Series is how you convert equation 7.9 to equation 7.10. I expect that you’ll need to know this like the back of your hand.

For the final parts of part (d), you’ll need a calculator. But at least you can set up the Formula for the Geometric Series correctly. And you can (without a calc) solve for the PDV when  the growth rate of income 

(a) If the interest rate is R, what is the formula for the present discounted value today (in year 0) of labo income from a particular future year t? 

The present discounted value of a wage in the future, is that future wage, discounted by the interest rate over the number of years.

(b) Now add up these terms from t=0 to t=45 to get a formula for the present discounted value of labor income. Your answer should look something like that in equation (7,9) 

(c)  Write your answer in part b so that it takes the form of the geometric series. a=?

(d) Apply the geometric series formula to compute the present discounted value for the case of R=0.04, R=0.03 and R=0.02. What weird thing happens when 

But just to double check that you’re setting it up right:

Note that with you have , the growth rate of income. Whenever the interest rate equals the growth rate of income you’ll end up with a result like this. So, what is the Present Discounted Value of 50K a year, growing at 2% with 2% interest – from ? Each year you get a PDV of $50K, thus the PDV of the flow is just  

(e) Comment on these results. 

As the interest rate decreases the present discounted value of one’s wages increase…