a & c have already been answered, mainly looking for help on b, d, e and f. Thank you so much! Mary spends all her budget on statistical software (S) and office supplies (O). Her preferences can be represented by the utility function: U (S, O) = 2 ln(S) + 3 ln(O). (a) Compute the marginal rate of substitution of software for office sup- plies. Is the MRS increasing or decreasing in S? How do we interpret this? (b) Find Mary’s demand functions for software and office supplies, QS (pS,pO,I) and QO (pS,pO,I), in terms of the price of software (pS), the price of office supplies (pO), and Mary’s budget (I). (c) Suppose that the price of software is pS = 2, the price of office supplies is pO = 3, and Mary’s income is I = 10. What bundle of software and office supplies (S, C) maximizes Mary’s utility? (d) Suppose the price of software increases to pS = 4. What bundle of software and office supplies does Mary demand now? (e) Given the price increase, how much income does Mary need to remain as happy (have the same utility) as she was before the price change? What bundle of software and office supplies would Mary consume if she had that additional income, given the new prices? (f) Going back to the situation in part (d) (pS = 4 and I = 10), de- compose the total change of software and office supplies demanded into substitution and income effects. In clearly-labeled diagram with software on the horizontal axis, show the income and substitution effects of the increase in the price of software. (hint: use the Slutsky equation)
a & c have already been answered, mainly looking for help on b, d, e and f. Thank you so much!
Mary spends all her budget on statistical software (S) and office supplies (O). Her preferences can be represented by the utility function: U (S, O) = 2 ln(S) + 3 ln(O).
(a) Compute the marginal rate of substitution of software for office sup- plies. Is the MRS increasing or decreasing in S? How do we interpret this?
(b) Find Mary’s demand functions for software and office supplies, QS (pS,pO,I) and QO (pS,pO,I), in terms of the price of software (pS), the price of office supplies (pO), and Mary’s budget (I).
(c) Suppose that the price of software is pS = 2, the price of office supplies is pO = 3, and Mary’s income is I = 10. What bundle of software and office supplies (S, C) maximizes Mary’s utility?
(d) Suppose the price of software increases to pS = 4. What bundle of software and office supplies does Mary demand now?
(e) Given the price increase, how much income does Mary need to remain as happy (have the same utility) as she was before the price change? What bundle of software and office supplies would Mary consume if she had that additional income, given the new prices?
(f) Going back to the situation in part (d) (pS = 4 and I = 10), de- compose the total change of software and office supplies demanded into substitution and income effects. In clearly-labeled diagram with software on the horizontal axis, show the income and substitution effects of the increase in the price of software. (hint: use the Slutsky equation)
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