Suppose you were offered a job in which you would work 8

Chapter 12, Problem 97

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Suppose you were offered a job in which you would work 8 hours per day for 5 workdays per week for 1 month at hard manual labor. Your pay the first day would be 1 penny. On the second day your pay would be two pennies; the third day 4 pennies. Your pay would double on each successive workday. There are 22 workdays in the 89. Multiplier Suppose that, throughout the U.S. economy, individuals spend 90% of every additional dollar that they earn. Economists would say that an individuals marginal propensity to consume is 0.90. For example, if Jane earns an additional dollar, she will spend 0.9112 = $0.90 of it. The individual that earns $0.90 (from Jane) will spend 90% of it or $0.81. This process of spending continues and results in an infinite geometric series as follows: 1, 0.90, 0.902 , 0.903 , 0.904 , p The sum of this infinite geometric series is called the multiplier. What is the multiplier if individuals spend 90% of every additional dollar that they earn? 90. Multiplier Refer to 89. Suppose that the marginal propensity to consume throughout the U.S. economy is 0.95. What is the multiplier for the U.S. economy? 91. Stock Price One method of pricing a stock is to discount the stream of future dividends of the stock. Suppose that a stock pays $P per year in dividends and, historically, the dividend has been increased i% per year. If you desire an annual rate of return of r%, this method of pricing a stock states that the price that you should pay is the present value of an infinite stream of payments: Price = P + P 1 + i 1 + r + Pa 1 + i 1 + r b 2 + Pa 1 + i 1 + r b 3 + g The price of the stock is the sum of an infinite geometric series. Suppose that a stock pays an annual dividend of $4.00 and, historically, the dividend has been increased 3% per year. You desire an annual rate of return of 9%. What is the most you should pay for the stock? 92. Stock Price Refer to 91. Suppose that a stock pays an annual dividend of $2.50 and, historically, the dividend has increased 4% per year. You desire an annual rate of return of 11%. What is the most that you should pay for the stock? 93. A Rich Mans Promise A rich man promises to give you $1000 on September 1, 2011. Each day thereafter he will give you 9 10 of what he gave you the previous day. What is the first date on which the amount you receive is less than 1? How much will you have received when this happens? SECTION 12.4 Mathematical Induction 827 month. There will be no sick days. If you miss a day of work, there is no pay or pay increase. How much would you get paid if you work all 22 days? How much do you get paid for the 22nd workday? What risks do you run if you take this job offer? Would you take the job?

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