Consider an individual that must decide how much to consume in a two-period model. Suppose that her preferences for…

Consider an individual that must decide how much to consume in a two-period model. Suppose that her preferences for…

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Consider an individual that must decide how much to consume in a two-period model.
Suppose that her preferences for present consumption (c₁) and future consumption (c₂)
can be characterized by the following utility function:
u(c₁, c₂) = C₁ +20√/₂
Assume that her income in the present period is M₁, her income in the future period
is M₂, and the nominal interest rate is i. Further, assume that the price index in the
present period (p₁) is 1 and the price index in the future period (p2) is
P2 = (1 + d)p1
where d is the rate of inflation.
(a) [6 marks] Derive this individual’s marginal rate of time preference (MRTP). What
does her MRTP say about her willingness to sacrifice future consumption for more
present consumption? Use an appropriate diagram with c₁ on the horizontal axis to ex-
plain.
(b) [9 marks] Solve for this individual’s optimal choice of c₁ and c₂ respectively. Is c₁
an increasing or decreasing function of d? What about c₂? What does the relationship
between c₁ and d say about the substitutability of c₁ and c₂? Explain.
(c) [5 marks] For what values of d will this individual be a saver? Explain.

Expert Answer:

Answer rating: 100% (QA)

a To derive the individual s marginal rate of time preference MRTP we need to calculate the partial derivative of the
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