HW_1 Answers - ECON 3910 Microeconomics Homework 1 Chapter...

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ECON 3910 – Microeconomics Homework 1: Chapter 1 1.Suppose the Social Security Administration would like to guarantee the purchasing power of social security payments to the elderly does not diminish. That is, the real value of the payments does not decrease. The CPI in 1990 was 130.7 and the CPI in 1998 was 163.0. How much does the Social Security Administration need to increase payments from 1990 to 1998 to accomplish this objective? Solution: Let P denote the nominal payments in 1990 and P + x the nominal payments in 1998, where x is such that the real value of payments in 1998 remains the same as in 1990. This requires that (100/130.7)*P = (100/163)*(P+x). Solving it for x one has x = (163/130.7-1)*P = 0.25*P. Thus, the level of payments in 1998 needs to be (1+ 0.25)P. 2.The nominal price of a 1990 laptop was $3,500 and the CPI that year was 130.7. The nominal price of a laptop in 1998 was $1,600 and the CPI that year was 163.0. By what percent has the real price of laptops changed? Solution: The real price of a laptop in 1990 is (100/130.7)*3500=2677.89 whereas the real price of a laptop in 1998 is (100/163)*1600=981.60. Hence, the percent change in the real
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