Macroeconomics Week 5 Tutorial Solutions

Fall 2012 Week 5 Tutorial Questions Solutions (Ch4)

Chapter 4: Q1: Macroeconomics P141 Numerical Problems #1 Q2: Macroeconomics P.141 Numerical Problems #4 Q3: Macroeconomics P.143 Analytical Problems #1 Q5: Macroeconomics P.143 Analytical Problems #2 Q1: A consumer is making saving plans for this year and next. She knows that her real income after tax will be $25,000 in both years. Any part of her income saved this year will earn a real interest rate of 10% between this year and next year. Currently, the consumer has no wealth (no money in the bank or other financial assets), and no debts. There is no uncertainty about the future. The consumer wants to save an amount this year that will allow her (1) make university tuition payments next year equal to $6,300 in real terms; (2) enjoy exactly the same amount of consumption this year and next year, not counting tuition payments as part of next year’s consumption; and (3) have either assets nor debts at the end of next year. Answer: First, a general formulation of the problem is useful. With income of Y1 in first year and Y2 in the second year, the consumer saves Y1 – C in the first year and Y2 – C in the second year, where C is the consumption amount, which is the same in both years. Saving in the first year earns interest at rate r, where r is the real interest rate. And the consumer needs to accumulate just enough after two years to pay for college tuition, in the amount T. So the key equation is (Y1 – C)(1 + r) + (Y2 – C) = T.

a. How much should the consumer save this year? How much should she consumer? Answer: Y1 = Y2 = $25 000, r = 10%, T = $6300. The key equation gives ($25 000 – C) 1.1 + ($25 000 – C) = $6300. This can be simplified to $25 000 – C =$6300/2.1 = $3000, which can be solved to get C = $22 000. Then S = Y – C = $25 000 – $22 000 = $3000. How are the amounts that the consumer should save and consume affected by each of the following changes (taken one at a time, with other variables held at...