Assignment: Consumer Choice
A. Alcoholic Beverages
Gabriel John Utterson has an alcoholic beverage budget of £300/year, all of which he spends on gin (G) and wine (W) at Jekyll & Hyde, his local pub. The price of gin is £2/glass and the price of wine £1/glass. His beverage utility function is U = 4GW.
1. Write the equation of Utterson's budget constraint.
2. Plot and label this relationship in graph. Put the G on the horizontal axis and be sure the horizontal scale goes to 200 and the vertical scale to 300.
3. What is the slope of the line you have drawn?
4. Give a two sentence economic interpretation of this slope.
5. In graph, carefully plot and label Utterson's indifference curve for U = 18,000.
6. Plot and label his indifference curve for U = 30,000.
7. Plot and label his indifference curve for U = 45,000.
8. Assuming Utterson is a utility maximizer, how much gin and wine does he consume each year?
9. Suppose the price of gin rises to £3/glass (the price of wine remaining the same). Draw and label his new budget line in graph.
10. What are his utility maximizing consumption quantities after the price change?
11. Suppose the price of gin rises to £5/glass (the price of wine again remaining the same). Draw and label Utterson's new budget line in Graph.
12. What are his consumption quantities after this price change?
13. In graph, connect the optimal consumption points identified in problems 8, 10, and 12. What economic relationship have you drawn?
14. Plot the gin price/quantity combinations from the same three problems in graph and connect the dots. Put price on the vertical axis. What economic relationship have you drawn?
B. Salad
Teresa Treehugger makes salads using weeds (W) and seeds (S) which she purchases from the local organic food store at prices PW = $.40/oz. and PS = $1.25/oz. Her weekly salad budget is $24.00, and last week she bought 10 ounces of weeds and 16 ounces of seeds. At the end of the week, her utilometer readings were as follows for the last ounce of each good: MUW = 20 and MUS = 25.
15. What inequality tells us that Treehugger did not maximize her salad utility? (A numerical answer please.)
16. True or False: Treehugger should have purchased more weeds and fewer seeds. ____________
17. Suppose Treehugger's budget function and indifference map were plotted in a diagram with W on the horizontal axis. At last week's consumption point, what were the slopes of her budget line and indifference curve (in absolute value)?
C. Unusual Budget Lines
The consumers below all live in Johnson City and spend $160/week on clothing (C) and food (F) combined. Both are continuous goods. The consumers patronize different stores, however, and therefore face different pricing structures. Plot the appropriate budget line in each case, being sure to label and number the axes. Put F on the horizontal axis. In all cases, the relationships have shapes different from the one in the canonical model presented in class. (Hint: check your text.)
18. Lyndon shops at TexMart where the clothing and food prices are PC = $20/article and PF = $10/lb. TexMart's owner is Lyndon's brother-in-law so he (Lyndon) gets five free pounds of food per week.
19. Walter shops at Big Train where the clothing price,
PC = $20/article, is the same no matter how many articles are purchased. Food, however, is $20/lb. for the first five pounds and then $6/lb. thereafter.
20. Van shops at Mulholland's Maxi-Market where the prices are PC = $20/article and PF = $10/lb. Each week he uses a coupon that gives him a 60% discount on the first five pounds of food purchased.
D. Unusual Indifference Curves
Draw the appropriate indifference map in each case. (The word "map" means that you have to draw at least two indifference curves.) Be sure to label and number all axes. Also use arrows (or other means) to indicate the direction of preference (i.e., whether utility increases or decreases as indifference curves move away from the origin). In all cases, the curves have shapes different from those presented in class. All products are continuous in quantity and are "goods" unless noted otherwise. (Hint: check your text.)
21. "At the Chatterbox Cafe, I always take two lumps of sugar with my cup of coffee, no more and no less." (Perfect compliments case. Assume, unlike the other cases, that unwanted quantities are not consumed.)
22. "I enjoy apples and oranges in small quantities. However, I begin to dislike apples if I eat more than six per day and to dislike oranges if I eat more than eight per day." (Satiation case. Assume conventional indifference curves when both products are "goods.")
23. "I get pleasure from both Pep and Cokesi, but I like Pep twice as much" (Perfect substitutes case.)
24. "I eat only bread and chocolate. If I consume up to four chocolates per day, one chocolate gives me the same utility as one bread slice. If I consume more than four chocolates per day, it takes two chocolates to provide the same utility as one bread slice." (Modified perfect substitutes case.)
25. "My utility increases by 20 utils each time I eat a pint of ice cream and decreases by 10 utils each time I eat a pickle.
(Perfect substitutes case with one "good" and one "bad.")
26. "My diet consists of green eggs and ham. I always get some satisfaction from an additional egg. Ham, however, I only enjoy up to a point. If I eat more than five slices in a day, I become indifferent to it." (Modified neutral good case.)
E. Cashews
Richard Maple purchases cashews at the West 13th Street Delicatessen. His monthly demand curve for this product is Q = 100 - 40P, where Q is measured in ounces and P in dollars.
27. Last June the deli charged $1.10/oz. for cashews. What is the maximum amount that Maple would have paid (in total) for the cashews he
purchased at this price?
28. How much consumer surplus did he obtain from the cashews he purchased?
29. Explain the number you have just obtained in one intuitive sentence (that uses the number).
30. Approximately how much consumer surplus did Maple obtain from the 20th ounce of cashews?
31. In what ways (if any) are consumer surplus and utility similar to one another? In what ways (if any) are they different?
F. Miscellaneous
32. Frances has a monthly bread and jam budget of $120. Last month she spent twice as much money on jam as on bread. Jam was $5/jar;
how many jars did she buy?
33. Les Coralgab, a utility maximizer, spends $40/month on oranges (X) and grapefruits (Y). His citrus utility function is U = 30X + 20Y. If oranges are 25% more expensive than grapefruits (PX = 1.25PY), how many grapefruits does he purchase each month to maximize his utility?
34. Joe Quotidian spends his $120/week food budget on meat (X) and potatoes (Y) which he always consumes in a fixed one-to-one ratio (i.e., X = Y). Last week the price of meat (PX) was $20/lb; this week it is $5/lb.; and next week it will be $2/lb. Potatoes are always $10/lb. Write the equation for Quotidian's meat demand function: X = f(PX).
35. Plot Quotidian's meat demand curve in graph using the given meat price data. Put PX on the vertical axis. (Hint: You don't need the demand equation to do this.)