FREC 424 Intro Problem Set
  1. Basic math & theory review:
    1. The CPI is 322 (1960=100); by what percent has it risen since 1960? (Careful!)
    2. When P=$5, demand Q=3,500; when P=$6, Q=3,200.  Calculate the arc elasticity of demand.
    3. If Q = 100 – 5(P) + 0.001(I), calculate the point elasticities of demand with respect to price P and income I when P=$12 and I=$10,000. 
    4. The figure to the right shows a demand system for three goods A, B and C with respect to the prices of each good and Income.  What is the effect of an increase in the price of good B in each panel (shift demand line left, shift right, move up along same demand line, move down)?
    5. What are the relationships between A, B and C (complements or substitutes)?
    6. What are the relationships between each good and Income (inferior, normal, luxury)?

  2. Estimate each of the following--the correct order of magnitude is sufficient--in your head, and briefly explain your thinking. Do not use a calculator or pencil-and-paper math, and don't get hung up on precision. (For example, since it's easier to multiply by tens than twelves, you would assume there are about 10 inches in a foot.) Look up numbers (population, national debt, speed of light, etc.) if you don't know them approximately.
    1. How fast does human hair grow in miles per hour?
    2. How many babies are born in the world each day?
    3. What is the current US National Debt per capita?
    4. What is the speed of light in feet per nanosecond?
    5. If a normally-proportioned man was 100 feet tall, how much would he weigh?
    6. If you built a cubic box to contain one mole of ping-pong balls, how long would its edge be?
    7. Your tire pressure should be 30 pounds per square inch. What is that in kilograms per square centimeter?
      What is it in metric tons per square kilometer?
    8. In a scale model of the solar system, the Sun is a basketball, Jupiter is a ping-pong ball, the Earth is a BB, and the distance between the Sun and Pluto is one mile.  What percentage of the one-mile-radius sphere enclosing the solar system is actual matter?

  3. Suppose you are a contestant on the old TV game show “Let’s Make a Deal.”  Monty Hall, the game show host, has you choose one of three curtains.  The grand prize behind one curtain is a fancy car; the booby prizes behind the other two curtains are live goats.  Monty knows what’s behind each curtain.  You choose a curtain, but before Monty opens it, he opens another curtain to reveal goats, and then asks if you want to switch your choice to the other unopened curtain or stick with your original choice.  Should you switch, or stick with your original choice?  Does it matter?  Explain.

  4. In the first half of the season, baseball player A has 70 hits in 300 at-bats, while B has 22 hits in 100 at-bats for a .220 average.  In the second half of the season, A has 35 hits in 100 at-bats, while B has 100 hits in 300 at-bats.  Who had the highest batting average in each half of the season?  Who had the highest overall batting average? 

  5. Suppose you have just died, and find yourself playing round after round of a dice game in a strange casino. In each play of the game, you call a number between one and six, and then roll three ordinary dice. If your number comes up on just one of the dice, the angel pays you 1 unit of joy, if it comes up on two of the dice he pays you 2 units, and if it comes up on all three dice he pays you 3 units. If none of the three dice come up with your number, you lose 1 unit of joy.
    Calculate the expected payoff for each play of this game. Are you in heaven or hell?

  6. If your accuracy in estimating linear measurements is ±10%, what is your accuracy in estimating volumes?  Explain.

  7. At the end of every holiday weekend there is usually a long traffic backup at the toll-booth at the south end of the NJ Turnpike. Once the traffic backs up more than about half a mile even the EZ-Pass cars are stuck with the regular toll-payers, and it can take an hour or longer for a car to crawl to the toll booth.

    Do a little research on the NJ Turnpike: what is the typical toll being paid? how many lanes leading to the toll? etc. Formulate some reasonable assumptions about the time it takes for a car to crawl through each mile of backup, the number of cars stuck in each mile of backup for that amount of time, and the aggregate economic cost of drivers' and passengers' wasted time. (You have sat in long backups; how much do you think the typical carload of people be willing to pay to avoid 30-, 60-, 90- or 120-minute delays?). At what point (miles of backup) does the aggregate hourly cost of the backup exceed the turnpike authority's hourly toll revenue? In other words, at what point would it be more efficient for the turnpike authority to suspend toll-collecting and simply wave cars through the tolls to shorten the backup?

  8. A babysitting coop allows yuppie families with young children to swap babysitting services--no unreliable teenage babysitters, no problem with paying cash and getting in trouble over withholding taxes!  When you want to go out, the coop puts you in touch with another family that is staying home and willing to sit your kids.  You pay them one coop coupon per hour per kid.  On nights when you stay home, you can earn coupons by sitting other peoples' kids.

    Suppose there are X coupons distributed among N families. If you were the manager of this babysitting coop, how would you address each of the following problems:

    1. You observe that families have a savings demand for coupons, and typically want to keep a bunch in reserve in case they need a night of babysitting at short notice. More families are willing to babysit than are willing to spend their babysitting coupons, so there's not enough babysitting going on. As the "central bank" managing this coop, how would you solve this problem?
    2. Suppose there are too many coupons circulating, so that more couples want babysitting and a night out than are willing to stay home and babysit. What would you do to boost the supply of babysitting? What will happen if you do nothing?
    3. Some peoples' kids are sweet little angels whom everyone loves to babysit, while other peoples' kids are uncontrollable hellions. The parents of the hellions complain that they can't find other families willing to sit their kids at the standard coupon rate. What would you do to insure these parents get their "fair" share of babysitting?

    Questions 9 and 10 are for class discussion only, and will not be graded.

  9. Suppose you are a doctor in a remote jungle village where 300 villagers have come down with the dread mahogus, a horrible fatal disease.  You have two available drugs to treat this disease, but patients can only take one or the other; the combination is lethal. 
    Drug A is 100% effective for people with O+ blood, but completely ineffective in people with other blood types.  Statistically, one-third of the villagers are O+, but you have no way to test individual patients’ blood types.  If you administer Drug A to the 300 patients, you are certain to save 100 people, but 200 will die.
    Drug B is 100% effective in patients with the alpha variant of the dread mahogus, but completely ineffective in treating other variants.   Statistically, there is a one-third chance this outbreak is the alpha variant, but you have no way to identify which variant has struck the village.  If you administer Drug B to the 300 patients, there is a one-third chance you will save all 300 people, and a two-thirds chance they will all die.
    Which drug would you choose, and why?

  10. The Army Corps of Engineers is considering two designs for storm barriers to protect a coastal area in Guam with three villages, each with 100 residents.  The systems cost the same.   In the event of a 10-foot storm surge (a once-in-a-century event) design A, a single-barrier design, has a two-in-three chance of saving everyone, but if it fails, all 300 people in the three villages will die.  Design B, a sequential-barrier design, would simply restrict the flooding to whichever village was in the direct path of the storm, so 100 people would be certain to die, but the villages would be okay.  Which design would you choose, and why?