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?

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