Analysis of Market and Public Policy Spring 2023

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Problem Set 1
(Chapters 2, 3, 4)
Questions 1-5.
Consider the following demand and supply relationships in the market for golf balls: Qd = 90 − 2P − 2T
and Qs = −9 + 5P – 2.5R, where P is the price of a golf ball, T is the price of titanium, a metal used to
make golf clubs, and R is the price of rubber.
Use this information for Questions 1-5.

  1. If R = 2 and T = 10, find the market-clearing price and quantity for golf balls. Show this equilibrium
    graphically.
  2. At the market-clearing price and quantity for golf balls obtained in Question 1, calculate the crossprice
    elasticity of demand for golf balls with respect to the price of titanium. Are golf balls and
    titanium are substitutes and complements? Is their relationship elastic or inelastic? Explain.
  3. Suppose that the government sets a maximum price of golf balls as P = 10 (when R = 2 and T = 10).
    Would this pricing cause how much of a shortage or surplus of golf balls?
  4. Suppose that the price of rubber increases to R = 4 and the price of titanium declines to T = 5. Find
    the new market-clearing price and quantity for gold balls. Show this equilibrium graphically and
    discuss the effects of these price changes, in comparison to R = 2 and T = 10, on the market-clearing
    price and quantity for golf balls.
  5. Suppose that the demand for golf balls is given as Qd = 70 − 2P + 0.5N where N is the number of golf
    players in thousands. Explain how the demand for golf balls would change when the price of a golf
    ball declines by $2 and there is a 20% increase in the number of golf players from 100 to 120
    thousands. Is this change in demand different from the change in demand when Qd = 70 − 2P?
    Explain why or why not. Show your analysis graphically.
    Question 6.
    Malthus (1766-1834) ominously predicted that food supply would fall short of population growth,
    resulting in mass hunger and starvation. But his prediction was proven wrong as shown in the below
    figure.
    Analysis of Market and Public Policy Spring 2023
    2
    (1) It is observed that cereal yield steadily increased while food price index sharply declined during
    1975-1980. Using the supply-demand framework, explain why this phenomenon may happen.
    Draw a S-D graph to illustrate your analysis.
    (2) It is also observed that during 2005-2008, cereal yield steadily increased while food price index
    drastically increased. Explain why this phenomenon may happen using the supply-demand
    framework. Draw a S-D graph to illustrate your analysis.
    Question 7.
    Explain what properties of consumer preferences over two goods X and Y are implied by each of the
    following description on indifference curves. Draw the indifference map to demonstrate your answer.
    (1) Indifference curves have a negative slope.
    (2) Indifference curves cannot intersect and are not thick.
    (3) The marginal rate of substitution is diminishing along down the indifference curve of a given
    level of utility.
    (4) An indifference curve can be a negatively sloped linear line or a L-shaped.
    (5) The slope of indifference curves when X=10 varies across individuals.
    Analysis of Market and Public Policy Spring 2023
    3
    Questions 8-14.
    Jane receives utility from consuming food (F) and clothing (C) as given by the utility function U(F,C)=
    2FC, where F denotes the amount of food consumed and C the amount of clothing consumed. The
    marginal utilities are MU(F)=2C and MU(C)=2F. The price of good is PF, the price of clothing is PC, and
    income is I. On a graph, draw the indifference map and the budget line. Then answer the following
    questions.
  6. Is the marginal utility of food diminishing?
  7. Is the marginal rate of substitution (MRS) of food for clothing diminishing?
  8. Find the equation for the Jane’s demand curve for food.
  9. Suppose that the price of food is $2 per unit, the price of clothing is $10 per unit, and Jane’s weekly
    income is $100. Find Jane’s optimal consumption basket of food and clothing when her utility is
    maximized.
  10. What is the Jane’s MRSfood, clothing when utility is maximized?
  11. Suppose that Jane receives an income subsidy in cash of $20 from the government. Find Jane’s
    optimal consumption basket. What is the maximized level of utility with this income subsidy?
  12. Suppose that Jane receives a discount coupon from the government, instead of an income subsidy of
    $20 (thus I = $100). With this coupon, Jane can purchase food at $2 for each of the first 10 units, but
    only $1 per additional unit. Find Jane’s optimal consumption basket. What is the maximized level of
    utility with a discount coupon? Is Jane better off with a discount coupon than with an income
    subsidy? Show your analysis graphically.
    Question 15.
    Sam lives on a diet of steak and potatoes. His budget is $50 per week. A potato costs $1 and the price of a
    steak is $10. Sam’s utility function, U=U(P, S) has a diminishing marginal rate of substitution of potato
    for steak where P is the amount of potatoes consumed and S is the amount of steaks consumed.
    (1) Draw Sam’s income-consumption curve of potatoes when potatoes are normal goods if the
    weekly income is $500 or less, but become inferior goods if the weekly income exceeds $500.
    (2) Suppose that the price of a potato declines to $0.5. Graphically show the substitution effect and
    the income effect of this price decline when it is a Giffen good. Draw the demand curve of a
    Giffen good (here, potatoes) and discuss why the Law of Demand fails.
    (3) Suppose that a potato tax ($0.1 per unit) is imposed. Explain the effect of this taxation on Sam’s
    optimal consumption of potatoes when it is a normal good.
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