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Assume the representative consumer lives in two periods and his preferences can be described by U(c,...

Assume the representative consumer lives in two periods and his preferences can be described by

U(c, c' ) = c ^(1/2) + β(c') ^(1/2) ,

where c is the current consumption, c' is next period consumption, and β = 0.95. Let’s assume that the consumer can borrow or lend at the interest rate r = 10%. The consumer receives an income y = 100 in the current period and y' = 110 in the next period. The government wants to spend G = 30 in the current period and G' = 35 in the future period.

1. Solve the consumer’s problem by finding the optimal allocations c* and c'*? .

2. Is the economy at the equilibrium? Explain

3. What are the equilibrium values of c and c'?

4. What is the equilibrium interest rate?

5. How will the equilibrium interest rate respond to an increase in G?

6. How will the equilibrium interest rate respond to an increase in G' ?

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