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

 

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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. 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.

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a To derive the individuals marginal rate of time preference MRTP we need to calculate the partial derivative of the utility function with respect to c2 and divide it by the partial derivative of the ... View the full answer