1) (12) Suppose demand for oil is given by Qd = 112 – 0.39P; supply for oil is given by Qs = 70 + 0.36P
a.What is the initial equilibrium price and quantity? What is the price elasticity of demand at this price?
b.What will the new equilibrium price and quantity be if due to shale development supply increases to 73 + 0.36P? What is the price elasticity of demand at this new price?
c.What happened to total expenditures on oil as a result of the change in supply?
d.Calculate the total consumer surplus before and after this change in supply.
2. Halloween is fast approaching, which means it’s time to think about costumes and that there will be a massive increase in demand for candy to give trick-or-treaters. Despite the massive increase in demand for candy, the price of candy does not increase near Halloween. This in contrast to roses, which experience a significant increase in price as Valentine’s Day approaches.
a.) Explain why the market for candy does not experience a significant increase in the price when demand increases, but the market for roses does.
b.) Use two separate graphs, one representing the market for roses on Valentine’s Day, and the other representing the market for Halloween candy on Halloween, to depict this situation.
c.) What do you think my 10-year old and 7-year old daughters should dress up as for Halloween this year?
3. Amazon had a dispute with the book publisher Hachette regarding its prices for e-books. Amazon tried to convince Hachette to lower their price for e-books, claiming that doing so would benefit both consumers and the publisher; Hachette refused to cut their prices, countering that lower prices would hurt both the publisher and their authors. Amazon explained their objectives in terms of price elasticity on their discussion board which they recently discontinued. Read the post (in the week 6 content folder) then answer the following questions.
a.) Amazon states that "For every copy an e-book would sell at $14.99, it would sell 1.74 copies if priced at $9.99." Use this information to calculate the price elasticity of demand for e-books between these two prices.
b.) Suppose Amazon was selling 7,000,000 Hachette e-books when the price was $14.99. If their above calculations are correct, how many would they sell after the price is cut to $9.99? What would the total revenue from e-books equal before and after the price cut? Show your work.
c.) Amazon claims that “e-books are highly price elastic.” If this is the case, then why wouldn't Amazon want to cut prices even further? For example, why not cut the price of e-books to $0.99 instead of $9.99?
d.) Given that Amazon is arguing that cutting e-book prices to $9.99 would benefit Hachette through higher revenue, why do you think Hachette was against this price cut? Briefly explain why Hachette may have been against the price cut, even if they did not dispute any of the estimates Amazon gives regarding the price elasticity of demand or revenue expectations.
4. The BLS conducts a Consumer Expenditure Survey on U.S. households to measure how they allocate their spending. The data for 2017-2019 is reported here: https://goo.gl/4VivHP
a.) What percent of annual expenditures did a typical consumer spend on Gasoline and other fuels (G) and everything else (Y) in 2018? Use this information to determine the typical consumer’s Cobb-Douglas utility function for Gasoline (G) and all other goods (Y).
b.) What is the formula for consumers’ marginal rate of substitution between gasoline and all other goods?
c.) The average price of gasoline has decreased from $2.75/gallon to $2.25/gallon. Given your utility function described in a., calculate the amount of gasoline purchased by a typical consumer in 2018 and 2019. Note, assume income equals average annual expenditures in 2019, and the price of all other goods is $1.
d.) Use the calculations from part c. to determine the price elasticity of demand of gasoline. Do you think this is a realistic value? Briefly explain.
5. Lillian likes to eat, eat, eat, Apples (a) and Bananas (b). Her utility function is given by: U = 5a + 2b, Apples cost $3 per pound, bananas cost $2 per pound, and she has $36 to spend.
a.) How many apples and bananas will she consume? What is her total utility?
b.) Suppose the price of apples begins to increase while her income and the price of bananas remains constant. At what price of apples would Lillian only eat bananas, and what is her utility?
6. Sarah always drinks vodka martinis in exactly the same way (her family thinks she has a drinking problem, which she ignores). She uses 2 parts vodka (V) and 1 part olive brine (O) in every drink.
a.) What is her utility function for vodka and olive brine?
b.) Sarah spends $30 on vodka martinis every night (come on Sarah, listen to your family, they love you!) and the prices of vodka and olive brine are $5 and $1, respectively. What is Sarah’s utility-maximizing bundle of vodka and olive brine (don’t worry if the quantity of drinks are not whole numbers)?
c.) Suppose the price of vodka increases to $6 while the price of olive brine decreased to $0.50. What is her new utility-maximizing bundle of vodka and olive brine? Does the change in her consumption reflect a substitution effect, an income effect, or both? Explain.
7. Connetquot High School, which is where I went to school (Go T-birds!) has $60,000 to spend on computers (C) and other stuff (Y), so its budget equation is given by C + Y =60,000, where C is expenditure on computers and Y is expenditures on other stuff. C.H.S. currently plans to spend $20,000 on computers and $40,000 on other things. The state wants to encourage computer literacy in all high schools. The following two plans have been proposed.
Plan A: Give a grant of $10,000 to each high school in the state that the school could spend as it wished.
Plan B: A “matching grant.” For every dollar’s worth of computers that a high school orders, the state will give the school 50 cents.
a.) Suppose that the headmaster’s preferences for expenditures on computers and other things are given by the utility function U=C0.5*Y. Calculate how much the headmaster will choose to spend on computers and other goods if it does not adopt any plan, under Plan A, and Plan B.
b.) Which would the headmaster prefer: No plan, Plan A or Plan B? Explain.
8. A consumer spends all their income on 2 goods, x and y. The price of x has increased. Show the tangencies representing consumer utility maximization before and after the price change. Decompose the change into income and substitution effects. Assume convex utility functions. Label everything in your graph clearly. Given the way you have drawn the graph, is the good normal or inferior? Explain.
9. Suppose a Lori’s demand is given by X=10 + I/10Px, where I =$120.
Px is $2 initially, then it increases to $3.
Calculate the change in consumption of X; how much of this change is due to the income effect and how much is due to the substitution effect?
10. Suppose the compensated price elasticity (e xc, px)= -0.7; share of expenditures on X (Sx)= 0.07, and income price elasticity (e x,I ) = 0.2. Calculate the uncompensated price elasticity, e x, px .
11. Suppose you go to Chuck-E-Cheese because someone told you they have the best food and service. Turns out they were wrong! The pizza is horrible and you receive very poor service (meaning you have a lower utility level). In one sentence each, describe your compensating variation and your equivalent variation associated with this experience.
12. Suppose the expenditure function is given by E=1.89*V*Px2/3*Py1/3, where E denotes expenditures and
V denotes utility.
a. What is the formula for the compensated demand for good X?
b. Initially, Px=$2 and Py=$1 and V=100. Then Px increases to $3, and V decreases to 76.4.
Calculate the compensating variation and equivalent variation associated with this increase in price.