Microeconomic Theory
Assignment 1:
1. Read the following short piece from The Economist: Daily chart - What's up, doc? - How much a doctor gets paid depends on where they live in America by N.L. & THE DATA TEAM
which discusses the determinants of doctor pay. It notes that "a doctor of general medicine in New York typically earns 64% less than a peer in Alabama." This is despite the fact that there is a significantly higher demand for general medicine in New York compared to Alabama. Use a single set of axes with separate supply and demand curves for medicine practitioners in New York and Alabama to depict this situation. Your diagram should depict that the demand for general medicine practitioners is higher in New York, while the salary of general medicine practitioners (the price for labor) is higher in Alabama.
2. Amazon recently had a very public dispute with the book publisher Hachette regarding its prices for e-books. Amazon was trying convince Hachette to lower their price for e-books, arguing that doing so would benefit both consumers and the publisher; Hachette was refusing to cut their prices, countering that lower prices would hurt both the publisher and its authors.
Amazon explained their objectives in terms of price elasticity on the following discussion board:
Read the full post then answer the following questions.
a.) Amazon states that "For every copy an e-book would sellat $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. Show your work.
b.) Suppose Amazon was selling 5,000,000 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?
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 Amazonis 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? Hachette obviously did not agree that this price cut would benefit them; but that does not mean they disputed what Amazon was saying. Briefly explain whyHachettemay 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.
3. Suppose Carmela's income is $100 per week, which she allocates between sandwiches and books. Sandwiches cost $2 each. Books cost $10 each if she purchases between 1 and 5 books. If she purchases more than 5 books in a week, the price falls to $3.33 for the 6th book and all subsequent books.
a.) Draw her budget constraint with books on the horizontal axis and sandwiches on the vertical axis.
b.) There is a potential issue with finding a unique utility maximizing tangency point for this budget constraint. What is that issue?
4. Lillian likes to eat, eat, eat, Apples (a) and Bananas (b), and sometimes she likes to uut, uut, uut, Upples and Bununus. Her utility function is given by: U = 12a + 3b, Apples cost $4 per pound, bananas cost $2 per pound, and she has $20 to spend.
a.) Show Lillian's indifference curve and budget line on a graph.
b.) How many apples and bananas will she consume? What is her total utility?
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?
5. In 2008, a typical year old consumer bought 34 music tracks at a cost of $1.00/track, and spent an average of $46 on live music.
a.) What is the typical consumer's Cobb-Douglas utility function, where music tracks are q1 and live music is q2.
b.) What is the formula for the typical consumer's marginal rate of substitution?
c.) In 2012, the standard price on i-tunes increased from $1.00/track to $1.29/track. Suppose the typical consumer still spends the same amount on all music, and the price of live music remained constant. How many music tracks will the typical consumer buy after this increase in price?
6. Connetquot High School, where I went to school (Go Thunderbirds!) 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 Education Commission wants to encourage computer literacy in all high. 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=C*Y2. 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.
Which would the headmaster prefer: No plan, Plan A or Plan B? Explain.
7. Read the following piece from fivethirtyeight regarding Uber usage in different neighborhoods:
Public Transit Should Be Uber's New Best Friend by Nate Silver and Reuben Fischer-Baum on fivethirtyeight website
then answer the following questions.
a. The third figure shows Uber usage by median income level. Use this information to plot out the basic shape of a typical consumer'sEngel Curve for Uber.
b. Use the statistics in table to calculate the income elasticity of demand for Uber from median income levels 100 - 125K, and 125 - 150 K (use the lower values as your base income). Is Uber a normal good or inferior good over these ranges? Briefly explain why it changes the way it does as income increases.
c. The fourth figure shows Uber usage by number of subway lines available in the census tract. Does this suggest that Uber and public transit are complements or substitutes? Explain.
8. Suppose the government wants to reduce consumption of cigarettes and liquor. It tries to do soby tracking all cigarette and liquor purchases for all consumers, then reducing consumers' income by their expenditures in the form of a lump sum tax - so if you spent $500 on cigarettes and liquor in a year your income would be lowered by $500 the next year.... Don't worry about the logistics of this policy).
Would this be an effective policyto reduceliquor and alcohol consumption? Why or why not. What might be a more effective policy to reduce consumption? Explain.
9. 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.
10. a.) Calculate e x, pxgiven the following: the compensated price elasticity (e xc, px)= -0.6; share of expenditures on X (Sx)= 0.07, and income price elasticity (e x,I ) = 0.2. Is this good normal or inferior?
b.) What happens to ex, pxas the share of expenditures on X increases? Explain why this happens.
11. The Ministry of Tourism in the Republic of Palau estimates that the demand for its scuba diving tours is given by Qd = 6,000 - 20P, where Q is the number of divers served per month and P is the price of a dive. The supply of scuba tours is given by Qs=30P - 2000.
a. Solve for the equilibrium price and quantity.
b. Calculate the value of consumer surplus received by divers visiting Palau at this equilibrium.
c. Calculate the price elasticity of demand at this equilibrium.
d. Suppose the demand increases toQd = 7,000 - 20P. Calculate the new level of consumer surplus.
12. Suppose you go to your favorite restaurant and receive very poor service and your meal is served cold. Describe your compensating variation and equivalent variation associated with this experience.
13. Suppose the expenditure function is given by E=1.89*V*Px2/3*Py1/3, where E denotes expenditures and V denotes utility; 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.