Economics Assignment
1. Suppose that you are doing field research in economics by tracking the consumption of cans of Red Bull of your roommate. During the first week of semester the price of a 12 oz. can was $3.00 and your roommate drank 5 cans. During the last week of the semester the price of the same 12 oz. can was $4.00 and your roommate drank 3cans.
a. Draw and label a consumer choice model (with "standard" indifference curves and budget constraints) that could have produced the resultsabove. For simplicity, make the other good in your model (C2) the numeraire and assume that its price is$1.
b. On the graph above, decompose the income and substitution effects associated with this price change. (Note: this is by labelingdifferent values of C1 (Red Bull) on the C1axis.)
c. Explain intuitively (not referencing your graph) what the incomeeffect means, i.e. how it factors into your roommate's consumptionchoice
d. Explain intuitively (not referencing your graph) what the substitution effect means, i.e. how it factors into your roommate's consumptionchoice.
2. Suppose that a government is considering three alternative ways to provide financial support for college students. Suppose for simplicity that the price per credit for all students in$500.
PLAN A: Offer tax credits that reduce the price per credit by 20 percent.
PLAN B: Give all students a voucher for 8 credits.
PLAN C: Give all students an extra $4,000 in cash.
a. If the average student's income is $10,000 per semester and C2 is a "composite" good with a price of 1, graph the budget constraint foreach plan.
b. Are there certain types of students who will receive higher utility onone plan versus another? Explain why or whynot.
c. Are all of the plans economically efficient? Why or whynot?
d. Which one would you recommend that the government adopt andwhy?
3. Consider consumption decisions of a consumer who likes hot dogs on hot dog buns - to the point where he will not eat a hot dog without a bun or a bun without a hot dog. She has an income of $30 per month to spend on these items. The price of hot dogs is $2 and the price of buns is$1.
a. Write down an equation for her budgetconstraint.
b. Draw a graph with her budget constraint and indifference curves. Put hot dogs (H) on the x-axis and buns (B) on the y-axis. Labelcompletely.
c. How many hot dogs and how many buns will she consume each month? Explain your answerintuitively.
d. Does her MRS between hot dogs and buns equal the price ratio at the solution you identified in part (b)? Why or whynot?
e. Now suppose that the price of hot dogs falls to $1. Illustrate the resulting change in demand for hot dogs and buns on yourgraph.
i. How will her consumption of hot dogschange?
ii. How will her consumption of bunschange?
iii. Which is more important in her reaction to the price change for hot dogs - an income effect or a substitution effect? Explainwhy.
f. Based upon your answers to part (e), how would you describeher elasticity of demand for hot dogs? Explain yourreasoning.
4. Answer these questions on a separate typed sheet (1 ½ or double spaced) that is stapled to the back of your problem set. You should write 1 paragraph for each question. Check out the Bureau of Labor Statistics website that is devoted to price indices and inflation for help with(b).
a. Explain in non-technicalterms (as you would to a friend who has never studied economics) and in no more than three sentences what the bias is in the traditional (Laspeyres) price index andwhy.
b. Why does the BLS compute a separate price index for medical care? How does the BLS computes this index? Explain why a medical care price index is inherently more complicated to construct than a price index for something like groceryitems.
5. Answer each of the followingquestions.
a. Suppose that an individual's utility function for income (M) is U = √M. Is this individual risk averse, risk neutral or risk seeking? Explain how you know (and show yourwork)
b. Draw a careful graph of this utility function. Label theaxes.
c. Construct a gamble that is more than fair (expected value>0)and demonstrate that this individual would takeit.
i. Explain the gambleitself.
ii. Show the expected value of thegamble.
iii. Show the expected utility of the gamble and compare it to utility without a gamble. Will this individual take thegamble?
6. You are thinking about purchasing a health insurance policy. Your income is $50,000. You face a 10% probability of getting strep throat and needing a doctor visit and antibiotics, which (together) would cost $1,000 if you had to pay out of pocket. You also face a 0.01% probability of being in an auto accident and needing hospital treatment, which would cost $20,000 if you hadto pay out ofpocket.
a. What would be the actuarially fair premium for this insurancepolicy?
b. Calculate the most that you would be willing to pay for this policy ifyou were risk-neutral. U = M.
c. Calculate the most that you would be willing to pay for this insuranceif you were risk-averse. U =M½
7. Consider the case of a car owner whose car is valued at $25,000. (You can consider $25,000 as his income in this problem.) Assume there isa 30% probability that he will be involved in a minor auto accident resultingin $5,000 in damage. Show graphically that if the consumer is risk averse he will prefer to be insured against this loss. Label carefully and explain your answer verbally.
8. As the owner of a family farm whose wealth is $250,000, you must choose between sitting this season out and investing last year's earnings ($200,000) in a safe money market fund paying 5.0 percent or planting summer corn. Planting costs $200,000, with a six-month time to harvest. If there is rain, planting summer corn will yield $500,000 in revenues at harvest. If there is a drought, planting will yield $50,000 in revenues. As a third choice, you can purchase AgriCorp drought-resistant summer corn at a cost of $250,000 that will yield $500,000 at harvest if there is rain and $350,000 in revenues if there is a drought. You are risk averse, and your preference for total family wealth (W) is specified by the relationship U (W) = √W. The probability of a summerdrought is 0.30, while the probability of summer rain is 0.70.
Which of the three options should you choose? Show all of your work and explain.
Bob is ready to buy his first home in the Seacoast region of New Hampshire. He attaches value to both the square footage of his new home and to the number of miles of hiking trails in the neighborhood. More specifically his preferences for square footage (F) and hiking trails (T) are given by his utility function:
U = FT
Plot at least one indifference curve to get the shape of Bob's indifference map. Hint: use graph paper and label carefully. Illustrate and describe Bob's optimal choice of square footage (F*) and hiking trails (T*) if he has $300,000 to spend on his house, PF = $100 and PH = $5,000. (Hints: MUF = T and MUT = F.)