Suppose the economy is populated by many identical agents. They live for two periods: t and t + 1. They act as price takers and receive exogenous amounts of current and future income, Yt and Yt+1. They solve a standard consumptionsavings problem which yields a consumption function Ct = C(Yt , Yt+1, rt)

(a) What are the signs of the partial derivative of the consumption function? Explain the economic intuition.

(b) Suppose there is an increase in Yt holding Yt+1 and rt fixed. How does the consumer want to adjust its consumption and saving? Explain the economic intuition.

(c) Suppose there is an increase in Yt+1 holding Yt and rt fixed. How does the consumer want to adjust its consumption and saving? Explain the economic intuition.

(d) Now let's go to equilibrium. What is the generic definition of a competitive equilibrium?

(e) Define the IS curve and graphically derive it.

(f) Graph the Y s curve with the IS curve and show how you determine the real interest rate.

(g) Suppose there is an increase in Yt . Show how this affects the equilibrium real interest rate. Explain the economic intuition for this.

(h) Now let's tell a story. Remember we are thinking about this one good as fruit. Let's say the meteorologists in period t anticipate a hurricane in t + 1 that will wipe out most of the fruit in t + 1. How is this forecast going to be reflected in rt? Show this in your IS Y s graph and explain the economic intuition.

(i) Generalizing your answer from the last question, what might the equilibrium interest rate tell you about the expectations of Yt+1 relative to Yt?

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Answer a The signs of the partial derivatives of the consumption function are CYt 0 This means that as current income Yt increases consumption C also ... View the full answer