# A company is considering whether to buy a new machine

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9. A company is considering whether to buy a new machine, which costs \$97,000. The cash flows (adjusted for taxesand depreciation) that would be generated by the new machine are given in the following table:Year1234Cash flow\$50,000\$40,000\$25,000\$20,000(a) Find the total present value of the cash flows. Treat each year’s cash flow as a lump sum at the end of theyear and use an interest rate of 7.5% per year, compounded annually.(b) Based on a comparison of the cost of the machine and the present value of the cash flows, would yourecommend purchasing the machine?10. You have the option of renewing the service contract on your three-year old dishwasher. The new service contractis for three years at a price of \$200. The interest rate is 7.25% per year, compounded annually, and you estimatethat the costs of repairs if you do not buy the service contract will be \$50 at the end of the first year, \$100 atthe end of the second year, and \$150 at the end of the third year. Should you buy the service contract? Explain.11. (Review Problems for Chapter 5-Problem 4) DemandDas a function of pricePis given byD=32-P. Find
510the inverse demand function.12. (Review Problems for Chapter 4- Problem 20) Solve the following equations fort.(a)x=eat+b(b)e-at=1213. (Review Problems for Chapter 5-Problem 5) The following function is strictly increasing in their domain. Findthe inverse and determine its domain.f(x) = 3 + ln(ex-2)
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Chapter 15 / Exercise 3
Principles of Economics
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3. Limits and Continuity1. Compute the following limits:(a) limx4x2-4xx2-3x-4=45(b) limh0(4 +h)2-16h= 8(c)limx→-414+1x4 +x=-116(d) limx1x6-1x10-1=35(e) limt01t-1t2+t= 1(f) limt→-2t2-4t2+ 10t+ 16=-232. Iff(x) =x2+ 2x, compute the following limits:(a) limx2f(x)-f(1)x-1(b) limh0f(2 +h)-f(2)h(c) limh0f(a+h)-f(a)h(d) limh0f(a+h)-f(a-h)hSolution:

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Chapter 15 / Exercise 3
Principles of Economics
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