Question

Lisa is a mother of two young children and devotes $100 per month to purchasing diapers and cheese. Cheese costs $5 per pound and diapers cost $0.50 each. a. Draw Lisa’s budget constraint, showing the quantity of diapers Q_D on the vertical axis and the quantity of cheese QC on the horizontal axis, and write down the corresponding algebraic expression. b. What is the relative price of a pound of cheese (in terms of diapers)? c. Suppose that Lisa’s utility function over her purchases of cheese and diapers can be expressed as U(C_C,Q_D) = Q_C^0.1Q_D^0.9. Her marginal rate of substitution between cheese and diapers is hence: MRS_C,D = (MUc/MUd= (0.1/0.9)(Qd/Qc). Solve for Lisa’s utility-maximizing level of consumption of diapers and cheese and illustrate this point in your figure from part (a). (Hint: Do not forget to apply Lisa’s budget constraint.) d. Under the U.S. Department of Agriculture’s Women Infants and Children (WIC) program, if Lisa’s family income falls below a specified threshold, she is eligible to purchase a variety of approved foods at no cost in order to support the development of her young children. Approved foods include a variety of dairy products, whole-grain foods, and fruits and vegetables. Suppose that in Lisa’s home state, she is eligible to obtain 5 pounds of free cheese per month. Illustrate how this modifies her budget constraint relative to what you drew in part (a). e. Now consider an alternative to the WIC program which simply provides a cash transfer to recipients in an amount equal to the value of their WIC food benefits. For simplicity, assume this program is limited to cheese, so that instead of receiving 5 pounds of cheese per month, Lisa would instead receive $25 (= 5 pounds cheese x $5/pound). Illustrate again how this $25 cash transfer affects Lisa’s budget constraint relative to what you drew in parts (a) and (d). f. In general, which type of benefit will leave recipients better off: the in-kind benefit (i.e., 5 pounds of cheese), or its cash-equivalent value ($25)? Why? Justify your answer in terms of the relevant aspects of constrained utility maximization. g. What will be Lisa’s utility-maximizing level of consumption of diapers and cheese with the $25 cash benefit? Illustrate this point in relation to the budget constraint drawn in part (e). h. What will be Lisa’s total utility at the utility-maximizing level of consumption (i) without any form of government assistance (part (c)), (ii) with WIC in-kind benefits, and (iii) with the $25 cash transfer (part (g))? What is Lisa’s most preferred outcome? (Hint: For (ii), how do you know that Lisa will be driven to a “corner solution” by the WIC program?) i. Why do you think the government chooses to provide in-kind benefits (food) instead of direct cash transfers?

Answer 1

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