Ricardian Equivalence VS Government with Money (30 Points). Suppose your friend who works as a consultant...

 

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Ricardian Equivalence VS Government with Money (30 Points). Suppose your friend who works as a consultant for the government in country A knows that you have taken ECON 102. He/She has to come up with a plan to stimulate economy. So, he/she decides to consult you about what the government in country A should do. The household in country A lives for only two periods. In each period, they are endowned with income y₁ and y2. They could choose to consume goods in period 1 or save to consume in the next period. If they choose to save, they will recieve a nominal interest rate of i. The household in country A also loves to hold cash. In this economy, cash serves as a storage of value but doesn't pay any interest rate. The household's utility function is: M₁ u(C₁, M₁, C₂) = log(C₁) + 0 log (11) + Blog(c₂) P₁ The household's budget constraint in each period is: Pici + Pia₁ + M₁ = P₁y₁ - PiTi P₂02 = P232 + P₂T2 + M₁ + (1+i) P₁a₁ a) (5 points, easy) Your friend proposes that government in his/her country can print more money to finance their spending. The new government budget constraint is the following: P₁G₁ + M₁ +(1+i) B₁ = P₁₁+ B₂+ M2. He/She further proposes that the amount of money print will be exponentially increasing at the rate of : Mt+1 = (1 + μ) Mt. Re-write the government budget constraint as a function of money demand, noting that money demand (for real balances) is Mª(Y,i) = . Since the government doesn't plan to borrow, you can drop B, from the budget constraint. b) (10 points, moderate) Note that the houshold has a utility from money that takes the form 6 (Mt) = 0 log - M₁ Pt We can derive money demand by using the following condition (you don't need to re-prove this, but it becomes evident from setting up the household's Lagrangian): M₁ 6 (141) = 1 + ₁ u' (C₁), 1+i where u(c) = log(c). Solve for money demand in terms of c₁. P₁ Ricardian Equivalence VS Government with Money (30 Points). Suppose your friend who works as a consultant for the government in country A knows that you have taken ECON 102. He/She has to come up with a plan to stimulate economy. So, he/she decides to consult you about what the government in country A should do. The household in country A lives for only two periods. In each period, they are endowned with income y₁ and y2. They could choose to consume goods in period 1 or save to consume in the next period. If they choose to save, they will recieve a nominal interest rate of i. The household in country A also loves to hold cash. In this economy, cash serves as a storage of value but doesn't pay any interest rate. The household's utility function is: M₁ u(C₁, M₁, C₂) = log(C₁) + 0 log (11) + Blog(c₂) P₁ The household's budget constraint in each period is: Pici + Pia₁ + M₁ = P₁y₁ - PiTi P₂02 = P232 + P₂T2 + M₁ + (1+i) P₁a₁ a) (5 points, easy) Your friend proposes that government in his/her country can print more money to finance their spending. The new government budget constraint is the following: P₁G₁ + M₁ +(1+i) B₁ = P₁₁+ B₂+ M2. He/She further proposes that the amount of money print will be exponentially increasing at the rate of : Mt+1 = (1 + μ) Mt. Re-write the government budget constraint as a function of money demand, noting that money demand (for real balances) is Mª(Y,i) = . Since the government doesn't plan to borrow, you can drop B, from the budget constraint. b) (10 points, moderate) Note that the houshold has a utility from money that takes the form 6 (Mt) = 0 log - M₁ Pt We can derive money demand by using the following condition (you don't need to re-prove this, but it becomes evident from setting up the household's Lagrangian): M₁ 6 (141) = 1 + ₁ u' (C₁), 1+i where u(c) = log(c). Solve for money demand in terms of c₁. P₁

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a Rewriting the government budget constraint in terms of money demand P1G1 M1 1iB1 P1Y1 B2 M2 Since ... View the full answer