School Evans of Public Affairs, Mark Long PBAF 516: Microeconomic Policy Analysis
Problem Set 2 -- Answers Consumer Theory 1) Tom consumes two goods, chips and salsa. Suppose the price of chips increases from Pc1 to Pc2. Carefully demonstrate the income and substitution effects of the price change on the consumption of chips under the following situations. For each of the following graphs the substitution effect will be shown with the closed arrow and the income effect will be shown with an open arrow a. Chips are normal goods:
b. The income elasticity of demand for chips is zero:
Note: Income effect = 0
Evans School of Public Affairs, Mark Long PBAF 516: Microeconomic Policy Analysis
c. Chips are an inferior good, but not a Giffen good:
d. Chips are a Giffen good:
Note: The size of the substitution effect is smaller than the size of the income effect and they're in opposite directions.
Evans School of Public Affairs, Mark Long PBAF 516: Microeconomic Policy Analysis
2) The government of Zanzinalia currently subsidizes the rent of its low-income citizens. The government pays 25% of the rent of its low-income citizens. Bob, who is considered to be lowincome, has $1,000 per month to spend on rent and other goods. He currently rents a $400 per month apartment, of which the government pays Bob's landlord $100 and Bob pays the remaining $300. The government is considering replacing its rent subsidy with a cash grant in the amount of $100 per low-income citizen. Assume that housing and other goods are both normal goods. a. Would Bob prefer the $100 cash grant or the $100 rent subsidy? Bob would at least be as well off with the cash grant as with the subsidy (since he could always use the cash grant to pay his landlord the full $100). In most cases, Bob will be better off, as he has discretion on how to use the $100. b. Show how Bob would change his consumption of housing and other goods after the subsidy is removed and the cash grant is given. Since Bob can afford his old bundle of housing and other goods, the policy change creates no income effect (i.e., his new budget constraint can exactly afford his old choice of housing and other goods). However, the price of rent has now effectively gone up since the subsidy is removed. Bob will then substitute towards other goods (which are relatively cheaper) and away from housing (which is relatively more expensive. c. Which program costs the government more money (assume Bob represents a typical low-income household)? Under the old program, the government was paying $100 for Bob's rent. Under the new program, the government is paying $100 to Bob. So, there is no change in the cost to the government. d. In the interest of economic efficiency, should the government use the rent-subsidy or the cash transfer? Are there other arguments you could make to support rent-subsidy over cash transfers or vice-versa? Since Bob is better-off, and the government is not worse off, the cash grant is more efficient. However, you might worry that Bob may use the $100 to purchase things that are not good for him or society (this is a paternalistic argument). 3) If sales taxes cause deadweight losses, why do we have sales taxes? There are two reasons that we might want to impose taxes: 1) To redistribute resources between groups in your society. A free market may be efficient, but not equitable. To generate higher equity, we could give the tax revenue to individuals who begin with lower endowments. However, we could nonetheless avoid the deadweight loss by simply taking a lump-sum from those with higher endowments and giving it to those with lower endowments, rather than imposing a tax on a market activity. In the real world, it can be difficult to know which individuals have higher endowments we then use a sales tax as a proxy for evidence of high endowments (under the assumption that those with high endowments have higher levels of purchases) . 2) To provide funds for public goods or to fix market failures these are issues we will discuss later in the term.
Evans School of Public Affairs, Mark Long PBAF 516: Microeconomic Policy Analysis
4) Define Pareto Effciency. Do you think this is an appropriate criterion for judging an allocation of resources? List at least one way in which it is inappropriate. Under what circumstances will a competitive equilibrium be Pareto efficient? A Pareto Efficient allocation of goods exists when there is no way to increase one person's utility without lowering the other's utility. A Pareto efficient allocation is a minimal criterion for a "good" outcome it ignores equity considerations. A competitive equilibrium will be Pareto efficient under the following circumstance: a) The market is competitive i.e., all market participants take the prices as given by the market and no one participant can affect or set the price. Furthermore all consumers pay only one price. Lastly, consumers can buy all that they want at the given price (there are no consumers who buy a large enough share of the goods to affect the price). b) There are no "externalities" to the consumption decision. An externality occurs when the welfare of one person is affected by the consumption decision of another person (e.g., driving and smog). c) Market participants have good information about the product's quality and prices of other goods. Browning and Zupan Problems: 4.1 A consumer's demand curve is the relation between the price of a good and the quantity of the good that the consumer would demand. We can derive the consumer's demand curve by changing the price of the good (holding constant other factors such as the price of other goods, the consumer's income, other and factors that affect demand) and finding the new quantity that the consumer would demand. This new quantity is found where the consumer's MRS = the new price ratio. 5.3 First, note that Kristine will be able to buy the same amount of Diet Coke (3 packs) and the same amount of other goods after this change in tax policy. Thus, she cannot be made worse off with this change. On the other hand, since the price of Diet Coke goes down, if Kristine gives up some amount of other goods, she will able to buy more Diet Coke than she was previously able to thus, she may decide to buy more Diet Coke and this could raise her utility. This is shown in the graph below:
8 7 6 5 4 3 2 1 0 0 2 4 6 Diet Coke 8 10 12 New Budget Set Old Budget Set
Other Goods
Evans School of Public Affairs, Mark Long PBAF 516: Microeconomic Policy Analysis
5.9 Suppose that Beth earns $100 this year and next. Now, suppose that she can borrow money (using her credit card) at a rate of 18% or she can save money in her bank's savings account, which pays 2% interest. Draw Beth's budget set by doing the following steps: 1) Plot her endowment point ($100, $100). 2) If she puts her whole $100 in the bank, consumes nothing in the first year, she would have $202 to spend next year ($100 * 1.02 + $100). This is the x-intercept. Connect the dots from the endowment point to the x-intercept. 3) If she consumes nothing in the second period, she could borrow up to $84.75 in the first year ($100/1.18). That is, if she borrows $84.75 in the first year, she will owe exactly $100 to repay her credit card. Adding this amount to her $100 in the first period yields $184.75 to consume in the first year. This is the y-intercept. Connect the dots from the endowment point to the yintercept and you are done.
Budget Constraint with ($100, $100) endowment, borrowing rate = 18%, lending rate = 2% 200
160 Slope = -1.18 120 C1 C2 80 Slope = -1.02 40
0 0 50 100 C2 150 200 250
Evans School of Public Affairs, Mark Long PBAF 516: Microeconomic Policy Analysis
5.10
Budget Constraint with ($6, $10) endowment, borrowing rate = lending rate = 25% 20
15 Slope = -1.25 C1 10 Optimal Choice = ($7, $8.75) Endowment 5
0 0 5 10 C2 15 20
Borrows $1 million, repays $1.25 million, C1 = $7 million, C2 = $8.75 million. Extension to problem 5.10: suppose the interest rate falls to 20% (for both borrowing and lending). How will this change affect the amount that Anna spends, borrows, and saves in each period? This change in interest rate will rotate the budget constrain clockwise (but still include her endowment). Her old optimal choice ($7, $8.75) will be inside the new budget constraint thus, she effectively has more income and will use it to increase both C1 and C2. Furthermore, first period consumption is now less expensive relative to second-period consumption (i.e., it costs less to borrow in the first period). So, she will substitute towards the relatively cheaper good (C1) and away from the relatively more expensive good (C2). Both the income and substitution effects point to more C1 thus, she will borrow more. C2 could rise or fall the income effect says C2 will increase, but the substitution effect says C2 will fall. 5.16 This individual's expected loss is the following: E(r) = 0.01*($100,000) + 0.99*($0) = $1,000. A risk-neutral consumer will not be willing to pay more than $1,000 for insurance. A riskadverse consumer wou...