Consider a two-period consumption model where an individual has income It > 0 in period t...

Consider a two-period consumption model where an individual has income I_t > 0 in period t and the (net) interest rate is r > 0. However, suppose the price levels are not assumed to be 1. Instead, let p₂ ≥ p₁ > 0.

(a) Derive the lifetime budget constraint.

(b) What is the slope of the lifetime budget line? Letting 1 + π = p₂/p₁ bethe gross inflation rate, given an interpretation of the magnitude of them budget line.

(c) Suppose p₂ = p₁ and I₂ = I₁ > 0 initially. Now, suppose there is inflation and the period 2 price rises to p′₂ = (1+π)p₁, where π > 0, while p₁ stays the same. Using a utility maximization diagram, show that an individual who was initially a borrower is made better off if her period 2 income also rises to I₂′ = (1 + π)I₂.

Expert Solution

Rahul Sunny answered 2 years ago

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