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# Solution: In each of 1 through 6, a function is given having period p. Compute the

ISBN: 9781111427412 173

## Solution for problem 14.79 Chapter 14

Advanced Engineering Mathematics | 7th Edition

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Problem 14.79

In each of 1 through 6, a function is given having period p. Compute the complex Fourier series of the function and then the 10th partial sum of this series at the indicated t0. Then, using N = 128, compute a DFT approximation to this partial sum at t0f (t) = t 3 for 0 t < 1, p = 1, t0 = 1/4

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Week 13 Thursday, April 14, 203:02 PM 4/12/16 Debt: -accumulated government borrowing over time. -How much money does the gov’t owe at this point in time -stock variable Deficit: -difference between government spending and tax revenue in a given period of time -new borrowing undertaken by government -flow variable 1) Inflation -tends to benefit borrowers and hurts lenders -may be easier for gov’t to pay off debts, eroding the real value of debt -π=ΔD/D real value of debt would not change. ΔD = reported deficit 2) Uncounted Liabilities -official debt/deficit numbers are understated because they exclude important gov’t liabilities -Social Security and Medicare, gov’t employee pensions -Contingent liabilities: student loans -gov’t could always change the rules 3) Capital Assets -some gov’t borrowing is used to purchase valuable assets -gov’t debt should account for assets as well as liabilities -official debt #s are overstate bc only include liabilities -not all govt assets can be easily liquidated 4) Business Cycle -During a recession, tax revenue goes down, gov’t spending goes up, which increases budget deficit (automatic) -During an expansion, tax revenue goes up, gov’t spending goes down, which decreases budget deficit - state of the economy affects budget deficit 5) Debt held by Public vs Total Government Debt -US govt owes a lot of money to: -Social Security Trust Fund -Medicare Trust Fund -Federal Reserve -Federal Financing bank -US govt owes a lot to itself 4/14/16 Week 13 Page 1 "Traditional" View of Gov't Debt LM -Increase in G or decrease in T r -IS shifts right -In short run, Y and r increase -Increase in r crowds out investment -In long run, less investment means less economic growth -therefore, there is a trade-off between short-run stimulus and long-run growth IS ' IS Y Ricardian View of Gov't Debt -Ricardian Equivalence: financing gov't spending via debt is equivalent to financing it via taxes -changes in fiscal policy will not have a big effect on consumption -forward looking consumers who want to smooth consumption -If gov't stimulates economy by deficit spending, at some point, G will decrease or T will increase to pay money back -A forward looking consumer would save money today because disposable income is lower in the future -low marginal propensity to consume -stimulus won't work bc Gov't multiplier essentially 0 Does Ricardian Equivalence Work 1) Consumer Myopia a. Consumers are not always rational and forward-looking 2) Borrowing Constraints a. People who can't borrow money now may have a high marginal propensity to consume 3) People have finite lifespans a. Gov't debt may be long-lived b. Households could have longer life spans Should the federal Government Have a Balanced Budget Amendment Pro: -fiscal policy is not a good way to stimulate the economy -politicians may put too much weight on short term gains Con: -automatic stabilizers increase deficit during a recession -certain infrastructure projects cost a lot up front, but pay off over time. Deficit spending facilitates this The government should try to balance its "structural" budget -what the budget would be without fluctuations of the business cycle Does Gov't Have an Effect on Monetary Policy -debt is usually easier to pay off with inflation -highly indebted governments may be tempted to generate inflation Week 13 Page 2 Week 13 Page 3

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