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HW4

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Econ 300
Assignment 4

  1. Suppose low-income people have preferences for nonfood consumption (NF) and for food consumption (F). In the absence of any income transfer programs, a person's budget constraint is given by

    $\displaystyle NF+P_{F}F=I$    

    where $ P_{F}$ is the price of food relative to nonfood items and $ NF$ and $ I$ are measured in terms of non-food prices (ie., dollars).

    1. Graph this initial utility-maximizing situation for this low-income person.

    2. Suppose now that a food stamp program is introduced that requires low-income people to pay $ C$ (measured in terms of nonfood prices) in order to receive food stamps sufficient to buy $ F^{\ast }$ units of food (presumably $ P_{F}F^{\ast }>C$ ). Show that this person's budget constraint if he or she participates in the food stamp program.

    3. Show graphically the factors that will determine whether the person chooses to participate in the program.

    4. Show graphically what it will cost the government to finance benefits for the the typical food stamp recipient. Show also that some people might reach a higher utility level if this amount were simply given with no strings attached.

  2. Suppose a person consumes only two goods, $ X$ and $ Y$ , and that the price of these goods are fixed. How would the set of utility-maximizing points traced out by successively higher incomes look if

    1. this person always split his or her income equally between $ X$ and Y?

    2. X were a luxury, Y a necessity?

    3. Y were a luxury, X a necessity?

    4. an unchanging amount of X were bought as income expanded above some minimal amount?

    5. X were an inferior good? (Can Y be inferior here too?)

  3. Ivan always buys left and right shoes in pairs. Explain why a sale on right shoes will have an income effect but no sustitution effect on his left and right shoe purchases.

  4. Suppose George doesn't care what type of toothpaste he buys. Show graphically why he will always buy the cheapest brand.

  5. Is the following statement true or false? Explain. ''Every Giffen good must be inferior, but not every inferior good exhibits the Giffen paradox.''

  6. When coffee prices rise, John buys more tea but fewer coffee mugs. Explain the substituion and income effects of the price change on these two goods.

  7. Elixabeth M. Suburbs makes $200 a week at her summer job and spends her entire weekly income on new running shoes and designer jeans, since these are the only two itmes that provide utility to her. Furthermore, Elizabeth insists that for every pair of jeans she buys, she must also buy a pair of shoes (without the shoes, the new jeans are worthless). Therefore, she buys the same number of pairs of shoes and jeans in any given week.

    1. If jeans cost $20 and shoes cost $20, how many will Elizabeth of each?

    2. Suppose that the price of jeans rise to $30 a pair. How many shoes and jeans will she buy?

    3. Show your results by graphing the budget constraings from $ a$ and $ b$ . Also draw Elizabeth's indifference curves.

    4. To what effect (income or substitution) do you attribute the change in utility levels between $ a$ and $ b.$

  8. Mr. Wright, a clothing salesman, is forced by is employer to spend at least $100 of his weekly income of $500 on clothing. Show that his utility level is lower that if he could freely allocate his income between clothing and other goods.

  9. The US Bureau of Labor Statistics periodically makes studies of family budgets and uses the results to compile the consumer price index (CPI). The tables below report total current consumption expenditures and expenditures on certain major categories of goods for 5 different income groups in the US in 1961. Group A is the lowest income group and Group E is the highest. Table 1 shows Expenditures by Category for various income groups. Table 2 shows percentage allocation of family budget by income group and category.

    (Table 1)Income Group A B C D E
    Food Prepared at Home 465 783 1078 1382 1848
    Food Away from Home 68 171 213 384 872
    Housing 626 1090 1508 2043 4205
    Clothing 119 328 508 830 1745
    Transportation 139 519 826 1222 2048
    Other 364 745 1039 1554 3490
    Total Expenditures 1781 3636 5172 7415 14208

    (Table 2) Income Group A B C D E
    Food Prepared at Home 26 22 21 19 13
    Food Away from Home 3.8 4.7 4.1 5.2 5.1
    Housing 35 30      
    Clothing 6.7 9.0      
    Transportation 7.8 14      

    1. Complete Table 2.

    2. Which of the goods are normal goods?

    3. Which of these goods satisfy the definition of luxury goods at most income levels?

    4. Which of these goods satisfy the definition of necessity goods at most income levels?


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Jenn Thacher 2008-08-25
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