Economics 222 Exercise B due Thursday 11 October in class

Size: px

Start display at page:

Download "Economics 222 Exercise B due Thursday 11 October in class"

Samuel Robertson
5 years ago
Views:

1 Economics 222 Exercise B due Thursday 11 October in class 1. According to the Labour Force Survey, in July 2001 there were thousand unemployed people in Canada and thousand employed people. The employment ratio was was 62.7 percent. (a) How many adults were not in the labour force? (b) What was the participation rate? (c) What was the unemployment rate? 2. Recently, both Canada and the United States have adopted chain weighting to calculate real GDP. An important feature of chain weighting is that it uses the previous period as a base, instead of some more distant period. (In the U.S. the base is the prior year, in Canada the prior quarter.) To capture the flavour of this change, look at the following model economy: Quantity Year 1 Year 2 computers 5 10 bicycles Price per unit computers bicycles (a) Suppose that year 1 is the base year. Find real output in each year and so find the growth rate of real output. (b) Suppose that year 2 is the base year. Find real output in each year and so find the growth rate of real output. (c) Statistics Canada recently switched from a 1997 base year to chain weighting. What qualitative effect would you expect this change to have on recent measurements of GDP growth? 3. [Hint: Reading parts of chapter 8 will make this question easy to do.] Baljinder s current income is y = 10, 000. Her future income is y f = 30, 000. There are only two time periods. Her plan is to set consumption at the same value in each year: c = c f. (a) If the interest rate is 3 percent, what value of consumption spending can she afford? 1

2 (b) Suppose that the interest rate rises to 6 percent. spending can she afford? Now what value of consumption (c) Suppose now that future income is less than current income: y = 30, 000 and y f = 10, 000. Find the values of consumption for each of the two possible interest rates. (d) Are your results consistent with the theory about the effect of a change in interest rates on saving and consumption? 4. In a closed economy, suppose that there are two time periods, denoted 1 and 2. In each time period, GDP is given by Y 1 = Y 2 = 300. This question studies the effects of fiscal policy in the first time period. Suppose that consumption depends on current and future after-tax income, as follows: C 1 = 0.43 ( Y 1 T 1 + Y 2 T 2 ). 1 + r Taxes in the first period are denoted T 1 and taxes in the second period are denoted T 2, while r is the real interest rate. To make this question simple, we ll suppose that the interest rate is fixed at 6%. (Question 6 examines the effect of fiscal policy on the interest rate.) (a) If G 1 = 30, T 1 = 30 and T 2 = 0 solve for C 1, S pvt and S govt. (b) Now suppose instead that the government has cut taxes to T 1 = 20. It financed its deficit by borrowing 10, and then introduces a tax in the second period of T 2 = 10(1 + r) in order to pay off its loan. Solve for C 1 under the new tax policy. (c) As a third scenario, suppose that the government instead spent G 1 = 45, and financed the increased spending by taxes. What is the effect on C 1, S pvt, and national saving of this change? 5. Imagine a closed economy in which Y = 120 and G = 12. Households set consumption according to C d = Y 300r, and firms plan investment according to where r is the real interest rate. I d = 0.2Y 100r, (a) Solve for r, C, and I in equilibrium when desired saving equals desired investment. (b) Suppose that because of a natural disaster G rises to 15. What is the effect on r, C, and I? 2

3 6. To rent or to buy? Dr. Gasthaus Maison is considering purchasing a house. She currently pays rent of $900 each month or $10,800 each year. She plans to purchase a house if the expected user cost is less than her current rent. The revenues from owning a house are not taxable, nor is the capital gain on a principal residence. The real interest rate is 4 percent. (We ll assume for simplicity that she faces this rate whether she lends or borrows.) She expects houses to appreciate in market value over the coming year by 4 percent. She expects the maintenance costs and property taxes incurred to be 5 percent of the value of a house. (a) What is the most expensive house she should buy? (b) If instead she expects house prices not to change during the coming year, then what is the most expensive house she should buy? (c) In the U.S., mortgage interest is tax-deductible, so that the effective interest rate is r(1 τ) where τ is an income tax rate. Suppose that this change in the tax law were introduced in Canada. If τ = 0.30 and a rise in house value is expected as in part (a), then what is the most expensive house Dr. Gasthaus Maison should buy? (d) What effect would you expect mortgage-interest deductibility to have on house prices? 3

4 Exercise B Answers 1. (a) N = thousand. (b) 67.59% (c) 7.23% 2. (a) With year 1 as the base year, Y 1 = 10, 000. For real output in year 2, we use the prices of year 1 and the quantities of year 2: Y 2 = 17, 000. Thus the growth rate was 70%. (b) When year 2 is the base year, Y 2 = 12, 000 since real and nominal GDP coincide for that year. Then we use the the year 2 prices to value year 1 quantities: Y 1 = Now the measured growth rate is 53.8%. (c) The numbers in this example are extreme, for easy calculation, but the ideas are realistic. We expect the switch to chain weighting to lead to some downward revisions of the measured GDP growth rate, at least for years when computer sales were strong, prior to When year 1 is the base year, computers are much more expensive than bicycles. The volume of computers grows more from year 1 to year 2 than does the volume of bicycles. So the overall growth rate of the economy is closer to the growth rate in the number of computers. Moving to a more recent year as the base (year 2) involves lower computer prices and so a lower weight on the growth in the number of computers sold. 3. (a) (b) (c) and (d) Yes. According to the theory, borrowers save more and consume less when the interest rate rises; that is found in parts (a) and (b). According to the theory, the effect of a change in r is ambiguous for lenders (because the income and substitution effects run in opposite directions); in this example we find an increase in r decreases Baljinder s saving. The aggregate effect probably is for an increase in r to increase saving slightly. 4

5 4. (a) C 1 = ; S govt = 0; S pvt = (b) C 1 = , S govt = 10, S pvt = This is an example of Ricardian equivalence. (c) C 1 = ; S pvt = S = 23.65; notice that the increase in government spending comes partly from a fall in consumption and partly from a fall in saving. (Incidentally, it also is predicted to affect the interest rate which we have ignored by fixing r = 0.06 an effect we ll see in question 5.) 5. (a) r = 8.5%, C = 92.5, I = (b) r = 9.25%, C = 90.25, I = (a) Here we solve which gives p k = 216, , 800 = ( )p k (b) With no appreciation expected, p k = 120, 000. (c) Now which gives 308, , 800 = ( ) p k 0.7 (d) Since this provision increases the demand for houses, it will raise house prices. This is an example of how a tax deduction becomes capitalized in asset values. 5

Queen s University Economics 222 Macroeconomics MID-TERM TEST

Queen s University Economics 222 Macroeconomics MID-TERM TEST Instructions: Answer 4 questions from Part A and 3 questions from Part B. Parts A and B are each worth 50 marks. You have two hours: budget