## 1. Sketch indifference curves for each of the following consumers for a day’s worth of coffee…

1. Sketch indifference curves for each of the following

consumers for a day’s worth of coffee and food, and describe why

the indifference curves take the shape they do. Draw the

indifference curves as how they would look if the drank a range of

0 to 4 cups. a. Ron treats coffee and food as ordinary goods, but

is neutral to coffee beyond 3 cups. b. For Gareth, food is always

an ordinary good where more is better; however, coffee is an

ordinary good up to 2 cups but then becomes a bad after two cups.

c. Julie only wants coffee and doesn’t care about food until she

has had 2 cups of coffee, after that both goods become ordinary

goods. 2. It is common for individuals and small businesses to join

stores like Costco to get lower prices. Suppose a consumer joins

Costco at a cost of $60 for an annual membership. Assume that

$1,000 is their allotted budget for goods at Costco and/or at all

other stores, but the stores offer the same goods. To simplify

assume that you can purchase goods at Costco and all other stores

in $1 increments. a. Graph the “budget constraint” for someone that

does not join Costco on a graph with Costco and All other Stores.

This is a little tricky, consider how many goods are bought from

All other Stores and Costco if they do not join Costco and quantify

the intercept. b. On the same graph, draw the budget constraint for

someone that joins Costco assuming Costco prices are 20% less

expensive than all other stores. If they join they can purchase at

Costco and All other Stores. Quantify the intercepts and slope of

the new constraint. c. Not everyone is made better off by joining

Costco. Draw an indifference curve for someone that would be

indifferent to joining Costco. This is a bit tricky, remember part

a. d. How much has to be spent at Costco to break-even for joining?

3. Evan has a choice of eating cookies or broccoli, but gives up

play time to do so. (Treat playtime as money that can be

interpreted as income or prices. When my son Evan was young he

would run around rather than eat with us. We threatened to reduce

his desert if he ran around during dinner. Of course this threat

was not credible so it did not work.) a. Currently his marginal

utility from broccoli is 15 and from cookies is 10. For each unit

of broccoli or cookies he eats he gives up 5 units of play time.

Should his consumption change? Explain using the last dollar rule

(the text refers to this as the use the graphs method on page 35).

Note, you do not have enough information to find an optimal bundle,

you can only say if his bundle is optimal or not and how he should

change consumption of each good if it is not optimal (not how much

he should change it) b. Suppose he gets less play time (income) and

eats the same amount of cookies, but less broccoli. Can you tell if

cookies and broccoli are normal, inferior, or income neutral? c.

Graph the change in part b. 4. Katie enjoys downloading music

tracks and attending live music. She pays PD = $1 per downloaded

song and PL = $10 per unit of live music (entrance fees to clubs).

She has $90 per month to spend on music. Her utility function for

music is U = D1/3L2/3, where D represents the quantity of

downloaded songs and L is live shows. a. Use either the Last Dollar

Rule (use-the-graphs pg 35) to find Katie’s optimal mix of music.

b. What is Katie’s level of utility at the optimal mix? c. One of

the weaknesses of using actual dollar values for prices and income

is that you cannot find Engle and Demand functions. Go back to part

a, but use the parameters M for income, PD for price of downloaded

songs and PL for price of live music and solve for the demand of

downloaded songs, QD = DD(PD, PL, M). d. Use the functions you

found in part c to take derivatives to show mathematically if

downloaded songs are: i. Normal or inferior? ii. Ordinary or Giffen

goods? iii. Are downloaded songs and live shows substitutes,

compliments or unrelated? Note, the derivative of DD(M, PD, PL)

with respect to PD is tricky, so don’t worry if you have

difficulty, give it your best try but don’t stress out. e. Graph

the Engle curve and the Demand curve for Downloaded songs on

separate axis using several prices and income levels. f. Find the

income elasticity of demand using the Dd function you found in part

c and a formula similar to the one two-thirds down on page 58 in

the text. g. The hardest relationship/function to find in this

problem is the utility function (income and prices are easily

observable). How would you set up an experiment to gather data on

someone’s utility function?