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- For an IS/LM model of an economy with the following equations: C = 200 + 0.8Yd | = 220 - 25i = 240 TR = 150 T= .2Y L=.1Y- 3i M= 125 The equilibrium interest rate and output combination is O (30, 1250) O (9.2, 1526) . O (69.5, 2168.4) (3, 125)(M/P)d = 1,000 − 100r,M = 1000P = 2.a) Graph the supply and demand for real money balances.b) What is the equilibrium interest rate?c) Assume that the price level is fixed. What happens to the equilibrium interest rate if the supply ofmoney is raised from 1,000 to 1,200?d) If the Central Bank wishes to raise the interest rate to 7 percent, what money supply should it set?Samantha Smoothie’s utility function is U(c1, c2) = c1c2, where c1 is her consumption in period 1 and c2 is her consumption in period 2. She earns $200 in period 1 and $220 in period 2. Samantha can borrow and lend at an interest rate of 10% and there is no inflation. The number of dollars that Samantha spends in the second period must be (C) a. more than 200 but less than 220. b. exactly 220. c. more than 220. d. exactly 200. e. less than 200.
- When analyzing how borrowing and lending affect the consumer's budget constraint, we measure spending in the current time period on the horizontal axis and spending in the future time period on the vertical axis. Assume that the interest rate at which the consumer can lend and borrow is 10%, income in period 1 is $1000 and income in period 2 is $1200. The point of maximum current consumption can be expressed as 1000+ 1200/1.1. 1000(1.1) + 1200. 1000+ 1200 + .1 1000/1.1 + 1200/1.1 + 1.Suppose Neha is a sports fan and buys only baseball caps. Neha deposits $3,000 in a bank account that pays an annual nominal interest rate of 5%. Assume this interest rate is fixed—that is, it won't change over time. At the time of her deposit, a baseball cap is priced at $10.00. Fill in the chart: 0% 5% 8% Number of Caps Neha Can Purchase after One Year Choices: 291, 305, 315, 582 Choices: 291, 300, 305, 582 Choices: 291, 305, 315, 582 Real Interest Rate When the rate of inflation is less than the interest rate on Neha's deposit, the purchasing power of her deposit __________ (options: falls, rises, remains the same) over the course of the year.Let the equilibrium condition for national income be ?(?) + ?(?) = ?(?) + ? (? ′ , ? ′ ,? ′ > 0; ? ′ + ? ′ > ? ′ ) Where S, Y, T, I and G stand for saving, national income, taxes, investment and government expenditure respectively. All derivatives are continuous a. Interpret the economic meaning of the derivatives ? ′ , ? ′&? ′ b. Check whether the conditions for the implicit function theorem are satisfied. If so, write the equilibrium identity c. Find ??̅ ?? and discuss its economic implications
- I always thought my good friend Rado Coetzee was quite original given his choices. He then once told me his utility function was U(c1,c2) = min {c1,C2} where c1 and c2 are his consumption in period 1 and 2 respectively. I know in the first period he earns $105 thousand and $168 thousand in period 2. Rado can borrow or lend at an interest rate of 10%. Inflation is negligible. What will he do? a) Rado will borrow 30 thousand dollars b) Rado will save 133 thousand dollars c) Rado will save 30 thousand dollars d) Rado will save all his money, buy a BMW X5 in Luxembourg, tax free, and never let his wife Inga drive it. e) None of the aboveSuppose Dariya is a fan of young-adult fiction and buys only young-adult books. Dariya deposits $4,000 into a savings account that pays an annual nominal interest rate of 5%. Assume this interest rate is fixed, and so it will not change over time. On the day she makes her deposit, suppose that a young-adult book has a price of $10.00. Initially, Dariya's $4,000 deposit has a purchasing power of young-adult books. For each of the annual inflation rates given in the following table, first determine the new price of a young-adult book, assuming it rises at the rate of inflation. Then enter the corresponding purchasing power of Dariya's deposit after one year in the first row of the table for each inflation rate. Finally, enter the value for the real interest rate at each of the given inflation rates. Hint: Round your answers in the first row down to the nearest young-adult book. For example, if you find that the deposit will cover 20.7 young-adult books, you would round the purchasing…A college professor is planning for his retirement years. His utility function is ?(?t , ?r ) = 3c t 0.5+2cr0.5 where ct represents his consumption today (period 1), his active years of teaching, and cr represents his consumption in his retirement years (period 2). During his active years of teaching, he makes a total of ₺3 million, while in his retirement years his total income is ₺1 million. He can borrow or lend at an interest rate of 25% between the two periods. Write an equation that describes the professor’s budget assuming he will spend all his income during his lifetime. If the professor chooses neither to borrow nor to lend during his active years, what will be his marginal rate of substitution between his consumption today and his retirement years? If the professor aims at maximizing his utility, how much does he consume in each period (use the Lagrangian method)? Does he save for his retirement years? If so, how much? At what interest rate would the professor…
- Suppose Latasha is a sports fan and buys only baseball caps. Latasha deposits $3,000 in a bank account that pays an annual nominal interest rate of 5%. Assume this interest rate is fixed-that is, it won't change over time. At the time of her deposit, a baseball cap is priced at $10.00. Initially, the purchasing power of Latasha's $3,000 deposit is baseball caps. For each of the annual inflation rates given in the following table, first determine the new price of a baseball cap, assuming it rises at the rate of inflation. Then enter the corresponding purchasing power of Latasha's deposit after one year in the first row of the table for each inflation rate. Finally, enter the value for the real interest rate at each of the given inflation rates. Hint: Round your answers in the first row down to the nearest baseball cap. For example, if you find that the deposit will cover 20.7 baseball caps, you would round the purchasing power down to 20 baseball caps under the assumption that Latasha…An IS curve shows: (a) that realized savings are most likely a function of interest rates, because changes in interest rates result in changes in precautionary demand for money; (b) the combinations of investments and incomes that result in the supply and demand for money being equal to one another; (c) the locus of all combinations of interest rates and incomes that will result in realized investment and realized savings being equal to one another; (d) that increases in output typically are caused by increases in interest rates.Given the information: Interest rate in US (Rh): Interest rate in UK (Rf): The current spot rate for GBP (SR₂): Suppose your lines of credit are USD 15,000,000 in the US and GBP 10,000,000 in UK. If your forecast tells you that the spot rate of GBP one year later (SR₁) will be $1.535, then your preferred investment strategy should earn a net profit of: OGBP 41,694 OGBP 200,000 USD 64,000 6% 4% $1.50 O USD 300,000