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

U(c,c)=c1/2+(c)1/2,

wherecis the current consumption,cis next period consumption, and= 0.95. Let's assume that the consumer can borrow or lend at the interest rater= 10%. The consumer receives an incomey= 100 in the current period andy= 110 in the next period. The government wants to spendG= 30 in the current period andG= 35 in the future period.

1. Solve the consumer's problem by finding the optimal allocationsc*andc*'.

2. Is the economy at the equilibrium? Explain.

3. What are the equilibrium values ofcandc?

4. What is the equilibrium interest rate?

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

6. How will the equilibrium interest rate respond to an increase inG?