Problem Set 1 Answers.doc

  • December 4, 2020

Introduction to Macroeconomics                                                                        New York University

Marc Lieberman                                                                                                Fall, 2014

Answers to Problem Set #1

(For Part II, see also the graphs in the separate pdf)

Part I

  1. From table: Equilibrium price = $40; equilibrium quantity = 500. 
  • Graph (solid lines for question #2)
  • We are looking for an equation of the form QD = A + B P.

“B” is the rate of change of QD relative to P (B = ∆QD / ∆P).  From the numbers in the table given in the problem, you can see that each time P rises by $10, QD falls by 250.  Therefore, B = ∆QD / ∆P = -250 / 10 = -25.  So B = -25.

“A” is the value of QD when P = 0.  You can extrapolate the numbers in the table to see that as P falls from $20 to $10 to $0, QD will rise from 1,000 to 1,250 to 1,500.  So A = 1,500.

Putting all this together, we see that QD = A + B P becomes QD = 1,500 ‑ 25P.

  • Set QD = QS, and solve for P:

                        100 + 10P = 1,500 ‑ 25P

                        35P = 1,400

                        P = 1,400/35 = 40

            Next, solve for Q, using either the supply or the demand equation (or both, to check your answer):

                        Q = 100 + 10(40) = 500

                        or

                        Q = 1,500 ‑ 25(40) = 500

  • The “rate of change” of one variable (Y) to another (X) is just ∆Y / ∆X.  This problem asks for ∆Q /∆P, so we use the equations for the demand and supply curves where Q is on the left hand side, and everything else is on the right.
    • For the supply curve,  ∆Q / ∆P = 10.
    • For the demand curve, ∆Q / ∆P is “B” or -25 (see the answer to question #3). 
  •  “Slope” always refers to the “steepness” of the line the way it is actually graphed, and is always equal to ∆ vertical-axis variable / ∆ horizontal-axis variable. In the graph, P is the vertical-axis variable, and Q is the horizontal-axis variable, so the slope of either the demand curve or the supply curve will be

∆P / ∆Q. This is the reciprocal of (or “one divided by”) ∆Q / ∆P.

  1. For the supply curve,  ∆Q / ∆P = 10, so the slope of the supply curve is the reciprocal of 10, or slope = 1/10 or 0.1
    1. For the demand curve, we already found (in problem 3) that ∆Q / ∆P is “B” or -25.  So, the slope of the demand curve = 1/B = -1/25 or -.04

An alternative method is to rearrange the supply and demand equations by solving for P on the left, and everything else on the right.  This puts the vertical variable on the left, and makes the slope appear in the equation.  Using this method:

Supply equation: QS = 100 + 10P , P = (QS – 100)/10 , P = -10 + (1/10) QS.

So, the slope of the supply curve is 1/10 or 0.1

Demand equation: QD = 1,500 ‑ 25P , P = (QD – 1,500) / (-25) , P = 60 – (1/25) QD.

So, the slope of the demand curve is –1/25 or -.04

  •  
    • The new demand equation will be: QD = (1,500 ‑ 25P) + 350, or QD = 1,850 ‑ 25P
    • To solve for P: 100 + 10P = 1,850 ‑ 25P , 35P = 1,750 , P = 50

To solve for Q:  Q = 100 + 10(50) = 600; or   Q = 1,850 ‑ 25(50) = 600

  • (see dashed line in graph)
    • Equilibrium price  has risen (from $40 to $50); equilibrium quantity has risen (from 500 to 600)

Part II

Note: The graphs and conclusions about P and Q are provided in the separate pdf  I’ve posted on the Aplia page.  This page explains the logic behind each graph, and possible alternative answers.

  1. The most assumption is that unusually heavy rainfall would decrease tastes for running, and therefore decrease the demand for running shoes at any price for them.  This is a leftward shift of the demand curve.  Other, less common assumptions could also apply, as long as they are stated clearly.  For example, if you assumed that rain would make people shift from wearing sandals to wearing running shoes, then the demand curve could shift rightward.  If you stated that rain interfered with the production of running shoes, the supply curve would shift leftward.  Thus, there is more than one correct answer, depending on your specific assumptions.  Only the most obvious (to me) assumption has been graphed.
  1. Most common assumption: By closing off two popular alternatives to running, more people would want to run and the demand for running shoes would shift rightward.  An alternative assumption (if stated clearly): people use running shoes when they bicycle.  If so, the demand for running shoes could shift leftward after bicycling is outlawed.
  1. This improvement in technology shifts the supply curve rightward, and has no impact on the demand curve.
  1. This increase in the price of an input (labor) shifts the supply curve leftward.  A less common assumption is that these workers are also buyers ofrunning shoes.  (In reality, running-shoe factory workers’ purchases would be an insignificant part of the entire market, so wouldn’t have much effect on the demand curve.  But, in theory, if the assumption is stated clearly, it can lead to a different answer. Under this less-common assumption, with the increase in their income, the demand curve could shift rightward.  But a correct answer must include the supply shift to the left.
  1. Recession, by decreasing household income, would shift the demand curve to the left (as long as running shoes are “normal” goods, which they no doubt are).  The hint in the problem was designed to steer you toward this analysis, rather than more complicated assumptions about how recessions might affect one or both curves.)
  1. The increase in tastes for running shoes in England would shift the demand curve for running shoes in England rightward, increasing their price there.  However, that is not the market we are depicting in our graph.  Instead, we’re graphing the market in the U.S.. But firms that sell running shoes in the U.S. can also sell them in England.  That is, running shoes sold in England are alternate goods for these firms. So, when the price goes up in England, then at any given price in the U.S., firms will want to sell fewer shoes in the U.S. than before (because they would prefer to shift more of their sales than before to England).  This is a leftward shift in the supply curve for running shoes in the U.S. (fewer running shoes offered for sale in the U.S. at any given price in the U.S.).
  1. When there is an anticipated price drop, sellers will want to sell more now before the price drops.  So at any given price now, more will be offered for sale. This is a rightward shift in the supply curve. At the same time, buyers will want to buy fewer shoes now, because they’d rather wait till the price drops.  So at any given price now, they will demand fewer running shoes than before—a leftward shift in the demand curve.  Note that while we know price will decrease, quantity could either increase or decrease, depending on which curve shifted more.

Part III.

  1. Official unemployment rate is 5/(98 + 5) = .048 or 4.8%.
  • The officially unemployed will now consist of two groups: (a) the 1 million that were “officially” unemployed before and are still “officially” unemployed, because they are still seeking work; (b) the 3 million newly laid-off workers who are seeking work and therefore added to the “officially” unemployed. Thus, there are 4 million “officially” unemployed.  The labor force is the new number employed (95 million) plus the officially unemployed (4 million).  Therefore, the official unemployment rate is 4 / (95 + 4) = .040 or 4.0%.
  • The number of “truly” unemployed increases to 8 million, consisting of three groups: (a) the 1 million that were “officially” unemployed before and are still “officially” unemployed, because they are seeking work; (b) the 3 million newly laid-off workers who are seeking work and therefore added as part of the “officially” unemployed; and (c) the 4 million who were “officially” unemployed before but are not counted as unemployed now, because they are “discouraged workers” and aren’t seeking work, even though they still want jobs.

The “true” labor force is the total of employed (95 million) plus the truly unemployed (8 million).  So the “true” unemployment rate becomes 8/(95 + 8) = .078 or 7.8%. 

  • In this example, the recession causes the “true” unemployment rate to rise (from 4.8% to 7.8%) while the official unemployment rate falls (from 4.8% to 4.0%).  Therefore, the official unemployment rate is giving us the wrong information about what is happening in the economy. This is an extreme example, but such perverse movements in the official unemployment rate do sometimes occur.
  • People who move from regular jobs to the underground economy are still working, so their “true” status has not changed: they are still employed.  The number of truly unemployed doesn’t change, nor does the “true” labor force. Therefore, the “true” unemployment rate remains unchanged.  The official unemployment rate, however, changes.  Official employment decreases to 98 ‑ 7 = 91 million.  Official unemployment increases to 5 + 3.5 = 8.5 million. (That is, official unemployment now includes the 5 million who were searching for work before, plus the 3.5 million underground workers who say they are searching for a job.)   Therefore, the “official” unemployment rate is now 8.5/(91 + 8.5) = .085 or 8.5%. This is an increase from the 4.8% we found in a. above.
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