Problem Set 1.doc

  • December 3, 2020

Introduction to Macroeconomics                                                                        New York University

Marc Lieberman                                                                                                Fall, 2014

Supplemental Problem Set #1

This problem set covers the algebra of supply and demand, and the connection between the algebra and the graphs.  It also has some problems on the unemployment rate.  Recitation this week (Friday, Sept. 12 and Monday Sept 15) will go through the algebra of supply and demand, which should help you answer these problems.

Do the problem set by the suggested “due date” posted in the Aplia course outline.  Some of the questions also appear as part of the Aplia problem set, but don’t ignore the other questions on this problem set – they are all important. Answers will be posted in the “Course Materials” section shortly after the due date.

You may have to struggle a bit for some of these questions.  But please wait to ask specific questions about the problem set until after you’ve had a chance to review the answers. Then, if you’re still confused about something, either (1) see me during office hours, or (2) email one of the TAs for an appointment.   [TA emails, and other information about recitations, are posted in a document in the “Course Materials” section of the Aplia course page.]  

Part I.  Suppose that the quantity of men’s dress shirts supplied and demanded in a market are as follows:

            Price                Quantity of                   Quantity of

            per Shirt           Shirts Demanded           Shirts Supplied

            $20                  1,000                           300

            $30                  750                              400

            $40                  500                              500

            $50                  250                              600

  1. Using only the data in the table, find the equilibrium price and quantity of shirts.
  • Carefully graph the demand and supply curves, and show the equilibrium price and quantity on your graph. [Note: put numbers on the graph & draw as accurately as you can. Use graph paper if it helps.]
  • The algebraic equation for the supply curve in the table above is:  QS  = 100 + 10P.  State the algebraic equation for the demand curve.
  • Using the equation for the supply curve given in question 3, and the equation for the demand curve that you found in question 3, solve for the equilibrium price and quantity algebraically (using only the equations)
  • What is the rate of change of quantity with respect to price (change in quantity per dollar change in price, or  ∆Q/∆P) on
    • …along the supply curve?
    • …along the demand curve?
  • What is the slope
    • …of the supply curve?
    • …of the demand curve?

[Note: be careful here.  A slope of a curve is always the change in the “vertical variable” divided by the change in the “horizontal variable,” as the curve is drawn. Outside of economics, graphs typically measure the dependent variable on the vertical axis.  But in supply and demand diagrams, the independent variable (price) is on the verticalaxis. So the slope of a supply or demand curve is always ∆P / ∆Q, not ∆Q/∆P.  To figure out the slope, you’ll have to manipulate the equation.]

  • Suppose that the demand curve shifts in such a way that, at every price, people want to buy 350 more shirts than before. 
    • What is the new equation for the demand curve?
    • Using the new demand equation, solve for equilibrium price and quantity algebraically.
    • Add the new demand curve to your graph, and graphically verify your answer in b. above.
    • State briefly what the demand shift has done to the equilibrium price and quantity (e.g., increase, decrease, unchanged).

Part II. With roughly drawn supply and demand diagrams (no graph paper necessary), illustrate how each of the following would affect the market for running shoes in the United States.  Carefully label all axes, curves, and points, and use general symbols for prices and quantities (e.g. P1 and Q2). [Note: there may be more than one correct way to answer.  If your answer makes special assumptions, write them down so you’ll remember what you were thinking later, when you check the answers.  All questions implicitly assume ceteris paribus.]

In addition to your graphs, state in each case what will happen to the equilibrium price and to the equilibrium quantity of running shoes (i.e., state increase, decrease, no change, or ambiguous for each of the two variables).

  1. There is unusually heavy and prolonged rainfall across the U.S.
  2. Bicycling and roller‑blading are outlawed in the U.S..
  3. There is a technological advance making running shoes easier and cheaper to produce.
  4. Workers in the factories that produce running shoes unionize, and win higher wages.
  5. The U.S. economy goes into recession – which, among other things, is a period during which household incomes decline.  (Hint: focus on the impact of declining income.)
  6. There is a dramatic increase in tastes for running shoes among people in England. (Hint: what happens to the demand curve for running shoes in England?  How will this affect the price of running shoes in England? How will this, in turn, affect the market for running shoes in the U.S., which is the market we are analyzing?)
  7. A newspaper article predicts that the price of running shoes in the U.S. will decline dramatically in the near future. Both producers and consumers of running shoes read and believe the article. 

Part III.

Suppose in a given month, 98 million people are working, and another 5 million want to work but aren’t working, and all of these 5 million are seeking work. 

  1. What would be the official unemployment rate, as reported by the U.S. Bureau of Labor Statistics (BLS)?

Now suppose that the economy goes into recession.  3 million workers are laid off and begin seeking work, while 4 million of those previously seeking work give up searching for jobs out of discouragement. 

  • What would be the new “official” unemployment rate as reported by the BLS?
  • Suppose we define the “truly” unemployed as the number of people who would like to work but are not currently working, and the “true” labor force as the sum of those working and those truly unemployed. After the recession hits, what would be the new “true” unemployment rate (the “truly” unemployed as a percentage of the “true” labor force?)
  • Compare how the recession has impacted the official unemployment rate and the “true” unemployment rate, and briefly discuss the implications of your finding.

Go back to the assumptions about employment and unemployment in a. above.  Now suppose that 7 million of the employed switch to jobs in the underground economy.  When interviewed by the BLS, 50% of these switchers report that they are not working and not seeking work, while the other 50% report that they are not working but are seeking work. 

  • What happens to the “true” unemployment rate (those who are truly not working anywhere but would like to work as a percentage of the true labor force)?  What happens to the official unemployment rate reported by the BLS?
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