Problem Set 5.doc

  • December 3, 2020

Introduction to Macroeconomics                                                                        New York University

Marc Lieberman                                                                                                Fall, 2014

Supplemental Problem Set #5

Note: To learn more about solving these types of problems, attend one of the recitations Friday Oct 24 or Monday Oct 27.

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:                            LS = 2 + 0.7 (W/P)

 LD = 62 – 0.8 (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): IP = 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 that problem set), and we’ll start with the same initial values for K, R, G and T as before. Specifically:

  • Capital stock is $10 trillion (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 (IP),  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 supply-side changes — each of which helps to increase potential output — occur all at once:

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

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

  • Due to technological advances, the production function changes to Y = 12 √(L x K x R)  

[Note: Notice the change from “10” to “12” in the production function. This will also 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 technological advances mentioned above, workers produce more output each hour 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: We’ll assume that the equations for S and Ip are not affected by any of these changes, and with no change in G or T or the deficit, there will be no change in the interest rate either.]

Solve for the new equilibrium values of L, W/P, and Y after all three changes occur.

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. “Although supply side changes like those in this problem can cause full-employment output to rise, the rise won’t be sustainable unless the government also buys more output.  Otherwise, the additional output won’t be purchased by anyone, and output will have to go back to its original level, before the supply side changes occurred.”  In the classical model (i.e., in the long run), is this statement true, false or partly true and partly false?  Explain.

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 (i.e., each hour of work produces $40 worth of products), average yearly hours are 2,000, the employment population ratio (EPR) is .60, and population is 250 million.  For the year in question, calculate:

(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 A and B, %∆ (AB) ≈ %∆A + %∆B.  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. 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.

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