1. Compare the following two pairs of goods: (1) Coke and Pepsi, (2) Plane tickets and hotel bookings

Transcription

1 ECNS 251 Homework 5 Consumer Theory 1. Compare the following two pairs of goods: (1) Coke and Pepsi, (2) Plane tickets and hotel bookings a. What is the relationship between Coke and Pepsi? What is the relationship between plane tickets and hotel bookings? Coke and Pepsi are substitutes while plane tickets and hotel bookings are complements. b. How will the indifference curves for Coke and Pepsi differ from the indifference curves for Plane tickets and hotel bookings? Why? Draw two separate indifference curve graphs (one for Coke and Pepsi and one for Plane tickets and hotel bookings), to illustrate the difference in the shapes of the indifference curves. Coke Hotel Bookings Pepsi Plane Tickets Indifference curves between Coke and Pepsi are fairly straight, because there is little to distinguish them, and they are nearly perfect substitutes. Indifference curves between hotel bookings and plane tickets are very bowed, because they are complements In the graphs above, the indifference curves illustrate perfect substitutes and perfect complements. In the graphs below, the indifference curves illustrate near (but not perfect) substitutes and complements. 1

2 c. For which pair of goods will consumers have a larger response to a change in the relative prices of each pair of goods? Why? A consumer will respond more to a change in the relative price of Coke or Pepsi. If they are perfect substitutes, the price change would imply that they would switch completely from one to the other. Consumers will be less responsive to a change in the relative price of hotels or plane tickets, since they often must be consumed in similar proportions. 2. You consume only soda and pizza. One day, the price of soda goes up, the price of pizza goes down, and you are just as happy as you were before the price changes. a. Illustrate this situation on a large, clearly labeled indifference curve and budget constraint graph. The figure below shows the effects of these price changes. If you are equally happy, you will remain on the same indifference curve. However, both the increase in the price of soda and the decline in the price of pizza make the budget constraint steeper. 2

3 b. How does your consumption of the two goods change? How does your response depend on income and substitution effects? You will consume less soda and more pizza. Since you remain equally happy, there is only the substitution effect to consider c. Can you afford the bundle of soda and pizza you consumed before the price changes? You can no longer afford your initial bundle. It lies outside of your new budget constraint 3. Head Coach of the New England Patriots Bill Belichick buys only defensive players and offensive players. a. In year 1, Bill s budget is $100 million, defensive players costs $3 million, and offensive players cost $6 million. Draw Bill's budget constraint. Offensive Players 16.6 BC Defensive Players 3

4 b. Now suppose that all prices increase by 10 percent in year 2 and that Bill's budget also increases by 10 percent. Draw Bill's new budget constraint. How would Bill's optimal combination of defensive players and offensive players in year 2 compare to his optimal combination in year 1? His new budget is 1.1*100million=110 million. Defensive players costs 1.1*$3 million=$3.3 million, and offensive players cost $6.6 million. His budget constraint does not change from year 1 to year 2. Offensive Players 16.6 BC Defensive Players 4

5 4. Consider a couple's decision about how many children to have. Assume that over a lifetime a couple has 100,000 hours of time to either work or raise children. The wage is $10 per hour. Raising a child takes 10,000 hours of time. a. Draw the budget constraint showing the trade-off between lifetime consumption and number of children. (Ignore the fact that children come only in whole numbers!) Show indifference curves and an optimum choice. The figure below shows the budget constraint. The initial budget line is shown as BL1. If all hours are spent raising children, 10 children can be raised. If all hours are spent working, $1,000,000 can be earned for consumption. The individual maximizes utility by choosing K1 children and a consumption level of C1. 1 b. Suppose the wage increases to $15 per hour. Show how the budget constraint shifts. Using income and substitution effects, discuss the impact of the change on number of children and lifetime consumption. If the wage rises, the budget line rotates to BL2 in the figure. The budget line is now steeper indicating the higher opportunity cost of raising a child. The substitution effect of this increase in the wage will mean a rise in consumption and a decline in the number of children. Assuming that both children and consumption are normal goods, the income effect of the increased wage will mean a rise in both children and consumption. The full effect on consumption is positive, but the end effect on children depends on the relative sizes of the income and substitution effects. c. We observe that, as societies get richer and wages rise, people typically have fewer children. Is this fact consistent with this model? Explain. If the number of children declines as incomes rise, the substitution effect must outweigh the income effect. 5

6 5. Suppose that Jed is currently consuming 4 donuts and 6 cups of latte per week. At this consumption bundle, the marginal rate of substitution between donuts and lattes is 2/3. In other words, Jed is willing to give up 2/3 of a latte in order to get another donut and still be just as well off as he was before. If the price of a latte is $3 and the price of donut is $4, is Jed behaving optimally? If not how should his consumption of donuts and lattes change? Three ways to get at the answer for this a. Jed willing to give up 2/3 of a latte in order to consume one more donut and still be just as well off as he was before. The cost that he has to pay to get a donut is 4/3 of a latte (if the price of a donut is $4 and the price of a latte is $3, giving up 1 donut frees up $4 to spend on lattes; $4 spent on lattes can by 1.3 lattes = 4/3 lattes), so Jed will be better off having fewer donuts and more lattes. b. Jed is willing to give up 2/3 of a latte in order to get another donut and still be just as well off as he was before. 2/3 of a latte gives as much utility as 1 donut In general, the change in utility one gets from consuming X is: U = X * MUx The change in utility he gets from getting 1 donut is: U = D * MUD = 1 * MUD The change in utility he gets from getting 2/3 latte is: U = L * MUL = 2/3 * MUL Since he stays just as well off, the change in utility from lattes and donuts must be equal: 1 * MUD = 2/3 * MUL So the MRS is: MUD/MUL = 2/3 If the MRS is: MUD/MUL = 2/3 and the price ratio is: PD/PL = 4/3, then the marginal utility per dollar spent on the two goods is: MUD/ PD = 2/4 =.5 MUL/PL = 3/3 = 1 Since a dollar spent on lattes yields more utility than a dollar spent on donuts, Jed should have more lattes and fewer donuts. c. The MRS (2/3) is the slope of the indifference curve (with donuts measured on the X-axis), while the price ratio (4/3) is the slope of the budget constraint. Since MRS < Price Ratio, the indifference curve is flatter than the budget constraint at this point. Point A in the graph below would coincide with a flatter indifference 6

7 curve than budget constraint. At point A Jed is not maximizing his utility. To increase utility from point A, he needs more lattes and fewer donuts. Lattes A Donuts 6. Read, "Why You'll Probably Pay More for Your Christmas Tree This Year," (New York Times 11/30/2017), and answer the following. a. Why is the Great Recession related to high Christmas Tree prices? b. Can the demand and supply model explain the movement in Christmas Tree prices over the past decade? What changes, and when? c. How do costs of production play a role in Christmas Tree production and how have they changed over time? 7