- November 30, 2020

Economics Principles I New York University

Marc Lieberman Fall, 2012

Supplemental Problem Set #5

Do the problem set on your own, but do *not *turn it in. Check your answers against the answers posted by the suggested due date on the Aplia course page. Please withhold any *specific *questions about this problem set until *after *you’ve had a chance to review the answers. Then, if you are still confused or troubled about something, either (1) see me during office hours, or (2) email one of the TAs to set up a meeting. [TA contact info is on the Aplia page, “Course Materials” section, in the document “TA & Recitation Info”]

Note: Recitation this week will cover problems similar to these.

**Part I: Supply Side Changes in the Classical Model**

Consider the numerical version of the classical model for a small country, from the previous problem set:

labor market: L^{S} = 10 + 5(W/P)

L^{D} = 70 – 10(W/P)

production function: Y = 10 √(L x K x R)

(Note: the square root sign might not print, but this says that output is ten times the square root of L x K x R. See what these variables mean below.)

Loanable funds market:

Household Supply of funds (Saving): S = 200 + 500r

Business demand for funds (Planned investment): I^{P} = 900 – 3000r

Government demand for funds: Depends on budget deficit (see below)

All variables have the same definitions as in the previous problem set (you might want to look at it), and we’ll start with the same initial values for K, R, G and T as before. Specifically:

- Capital stock is $10 billion (so “K” = 10)
- Land is 33⅓ billion acres (so “R” = 33⅓)
- G = $200 billion (so “G” = 200)
- T = $200 billion (so “T” = 200)

1. As practice, solve for the initial equilibrium values of employment (L), the real wage (W/P), total output and income (Y), the interest rate (r), saving (S) and planned investment (I^{P}), as you did in the previous problem set.

2. Draw a very rough graph of the three parts of the classical model (labor market, production function, and loanable funds market). Don’t worry about graphing to an accurate scale, but add numbers in the appropriate places on your graph for each of the equilibrium values you found in 1. above.

3. Now suppose the following three changes occur all at once:

- Due to a change in tastes, 3 million more people than before want to work at any given wage rate.

[Note: This will change the labor supply equation and shift the labor supply curve in your graph.]

- Due to a change in technology or an increase in the capital stock resulting from prior years’ investment spending, the production function changes to Y = 12 √(L x K x R)

[Note: This change will affect the appearance of the production function in your graph: more output than before can be produced using any given quantity of labor except for L=0.]

- Due to the same change in technology, workers are now more productive than before, so firms want to hire more workers at any given wage rate. Specifically, at any given wage rate, firms want to hire 15 million more workers than before.

[Note: This will change the labor demand equation and shift the labor demand curve in your graph.]

[Note: *each *of these three supply-side events would increase total output if it occurred by itself, so output will also increase when all three events occur at the same time.]

Solve for the new equilibrium values of L, W/P, and Y.

[Note: We’ll assume that the equations for S and I^{p} are not affected by any of these changes, and with no change in the deficit, there will be no change in the interest rate either.]

4. Add the relevant shifts and changes to the curves in your graph, and add numbers in the appropriate places for each of the equilibrium values you found in 3. above.

5. A fellow student who missed the lecture on Say’s Law has completed parts 1, 2, 3, and 4 in this problem, and says, “The new value I found for Y can’t possibly be a new equilibrium for total output, because it’s more output than before, but total spending hasn’t changed. Specifically, neither G nor I^{P} has changed, and saving hasn’t changed either (there was no change in the investment or saving equation, no change in the deficit, so no change in the interest rate or total saving). Therefore, no sector of the economy is spending more than it did before. If firms are producing a new, higher level of output, but spending hasn’t risen, then firms won’t sell all they are producing, so this new, higher level of output isn’t sustainable.”

This student is making an error. Find the error, and prove that this student is wrong by showing that total spending rises to equal the new, higher total output. (That is, show that Say’s law still applies.)

[Hint: Calculate the new level of consumption spending, then use it to calculate *total* spending, and compare total spending to total output. For hints on calculating consumption spending, see the previous problem set.]

**Part II. Using the Long-Run Growth Formulas**

For the each of the following questions, you’ll be using an equation that breaks down into its components one or more of the following variables:

- Total output
- Total output per capita
- The percentage change in total output
- The percentage change in total output per capita

Note: For more information on these formulas, refer to your lecture notes or pp. 235 – 238 of your textbook.

1. Suppose that, during a given year, productivity equals $40, average yearly hours are 2,000, the employment population ratio (EPR) is .60, and population is 250 million. Calculate for the year in question

(a) total output

(b) total output per capita

2. Suppose that, due to immigration, the population rises from 250 million to 300 million, but there is no change in productivity, average hours, or the EPR (i.e., these have the same values as in the last problem). Calculate (for the new population):

(a) total output

(b) total output per capita

(c) the percentage change in total output caused by the rise in population.

[Hint: There are two ways to do this. One is to calculate the answer directly, by calculating the new and the old total output and then the percentage change. The other is to use the approximation rule which says that for any two variables X and Y, %∆ (XY) ≈ %∆X + %∆Y. Both methods will give you the same answer. ]

(d) the percentage change in total output *per capita *caused by the rise in population

[Hint: There are two ways to do this. See the note above]

3. Suppose that, once again, population is back at 250 million, and all other values are as in problem 1. But over the year, productivity rises from $40 to $50. Calculate (for the next year):

(a) total output

(b) total output per capita

(c) the percentage change in total output caused by the rise in productivity (two ways to calculate the answer)

(d) the percentage change in total output per capita caused by the rise in productivity. (Two ways to calculate the answer)

4. Based on your answers in 1, 2. and 3. above, evaluate the following statement: “Increases in productivity and immigration both contribute to economic growth. With more people, we produce more output, which raises living standards. With greater productivity, each person produces more, which raises living standards.” Is this statement true? False? Or partly true and partly false? Explain briefly.

5. Suppose that, over a given multi-year period, productivity is rising by 2% per year, population is rising by 1% per year, average hours are falling by 0.5% per year, and the growth rate of the EPR is zero. Using the approximation rule, calculate the

(a) (annual) growth rate of total output

(b) (annual) growth rate of total output per capita

6. Suppose that, as in problem 5, average hours are falling by 0.5%. But now the growth rate of population is 2% per year, while the growth rate of productivity is 1% per year. Calculate the new

(a) (annual) growth rate of total output

(b) (annual) growth rate of total output per capita

7. Based on your answers in 5. and 6. above, evaluate the following statement: “Changes in the population growth rate or the productivity growth rate can each affect total output and living standards.” Is this statement true? False? Or partly true and partly false? Explain briefly.