2. Consider an economy consists of three types of economic agents who live for two periods. Their utililty function is given by u (c1, 2) = loge+ B log e where 3€ (0, 1). Workers differ by their income stream, which is exogenous. type X y1=2 and y=2 type-Y y1=4 and y=0 type-Z =0 and y2=4 There is a capital market with interest rate r = . (a) Solve for the optimal consumption of cach type. What is the ratio between e and e? Does this ratio differ by type? Explain. (b) Compare the optimal consumption level of each type. Who consumes the most? Provide economic interpretation of your results. (c) Suppose the government imposes capital taxes TK > 0. Find the equilibrium consumption (či, ö2) for type-X. Does your answer differ from the previous results in (a) and (b)? Why or why not?
2. Consider an economy consists of three types of economic agents who live for two periods. Their utililty function is given by u (c1, 2) = loge+ B log e where 3€ (0, 1). Workers differ by their income stream, which is exogenous. type X y1=2 and y=2 type-Y y1=4 and y=0 type-Z =0 and y2=4 There is a capital market with interest rate r = . (a) Solve for the optimal consumption of cach type. What is the ratio between e and e? Does this ratio differ by type? Explain. (b) Compare the optimal consumption level of each type. Who consumes the most? Provide economic interpretation of your results. (c) Suppose the government imposes capital taxes TK > 0. Find the equilibrium consumption (či, ö2) for type-X. Does your answer differ from the previous results in (a) and (b)? Why or why not?
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.12P
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Transcribed Image Text:2. Consider an economy consists of three types of economic agents who live for two periods. Their utililty
function is given by
u (c1, c2) = loge + ß log o
where 3 € (0, 1). Workers differ by their income stream, which is exogenous.
(type-X 1=2 and y2=2
type-Y y1=4 and y2=0
type-Z 1=0 and y=4
There is a capital market with interest rate r =
(a) Solve for the optimal consumption of each type. What is the ratio between c1 and ez? Does this
ratio differ by type? Explain.
(b) Compare the optimal consumption level of each type. Who consumes the most? Provide economic
interpretation of your results.
(c) Suppose the government imposes capital taxes TK > 0. Find the equilibrium consumption (č1,
č2) for type-X. Does your answer differ from the previous results in (a) and (b)? Why or why
not?
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