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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...

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Economics

Assume the representative consumer lives in two periods andhis preferences can be described
by U(c, c')=c^(1/2)+β(c')^(1/2)
where c is the current consumption, c' is next periodconsumption, and β = 0.95. Let’s assume that the consumer canborrow or lend at the interest rate r = 10%. The consumer receivesan income y = 100 in the current period and y' = 110 in the nextperiod. The government wants
to spend G = 30 in the current period and G' = 35 in thefuture period.

1. Solve the consumer’s problem by finding the optimalallocations c^* and c^(l*). [10 points]
2. Is the economy at the equilibrium? Explain. [05points]
3. What are the equilibrium values of c and c'? [05points]
4. What is the equilibrium interest rate? [05 points]
5. How will the equilibrium interest rate respond to anincrease in G? [05 points]
6. How will the equilibrium interest rate respond to anincrease in G'? [05 points]

Answer & Explanation Solved by verified expert
3.9 Ratings (624 Votes)
Uc cc12c12 095 y 100 y 110 G 30 G 35 r 10so Uc cc12095c12A solving for c and c maximise Ucc subject to c c1r y y1r that is the present value of total consumption mustbe equal to the present value of income    See Answer
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