Economics 222 Exercise A due Thursday 27 September in class

Transcription

1 Economics 222 Exercise A due Thursday 27 September in class 1. To answer this question, start by retrieving (from CANSIM) GDP at market prices for Ontario (D24082) and Québec (D24363) for Next, retrieve population for each province (D7 and D6), by converting to annual frequency using the average method. (a) Make a table showing nominal GDP per capita for each province and year. Be sure to state the units. (b) Also tabulate the three growth rates in nominal GDP per capita for each province. (c) During this period, were differences in the growth rates of GDP per capita between Ontario and Quebec mainly due to differences in GDP growth or in population growth? 2. Many commentators have predicted that economic growth in Canada will increase once firms begin rebuilding inventories. This question looks at some of the evidence. (a) Retrieve Canadian real GDP (in 1992 dollars) D and business investment in inventories (D100116) quarterly since the beginning of Use a table or graph to display the two series. Has inventory investment declined as a share of GDP? (b) How could you judge whether any decline in inventory investment has been unusually large? Would finding an unusually large decline mean that you had found the cause of the current slowdown? 3. Suppose that the U.S. has a current account deficit of 2.4% of GDP. Also suppose that investment as a share of output is 16.3% of GDP. (a) What is the U.S. national saving rate? (b) If government saving is 2.0% of GDP then what private saving as a share of GDP? (c) A macroeconomic forecaster writes: We predict that the U.S. current account deficit will widen to 3.0% of GDP next year because of the strong dollar. We also predict that that government saving (the budget surplus for all governments) will fall to 0.5% of GDP because of tax cuts. What is the forecaster implicitly predicting for the difference between private saving and investment, as shares of GDP? 4. Real interest rate are affected by the fact that nominal interest income is taxable. Suppose that interest income is taxed at a constant rate τ for all savers. (a) Write an expression for the after-tax, real interest rate. (b) Suppose that the federal government plans to issue bonds that guarantee a constant real return, after taxes. Suppose that the tax rate is τ = 0.3. By how much will the government need to alter the nominal interest rate on these bonds for each percentage point change in the rate of inflation? 1

2 5. Suppose that Singapore has the following production function: Y = AK 0.3 N 0.7. Suppose that the capital stock was 90 in 1975 and 320 in Over the same period, output rose from 200 to 600. (a) An economist believes that the labour input was 30 in 1975 and 42 in What is the economist s estimate of total productivity growth over this period? (b) Productivity sometimes is measured by output per worker rather than TFP. What is her estimate of the growth in output per worker? (c) Further research shows that, in fact, the labour input in fact rose from 30 to 50 due to increased participation in the labour force by women. How does this revised estimate affect estimates of growth in total factor productivity and in output per worker? (d) In each of these cases you have found a growth rate over twenty years. Find a formula to convert any of these growth rates to the corresponding implicit growth rate per year. (Hint: Think of compound interest.) 6. Profit-maximizing, competitive firms have the production function Their current capital stock is K = 200. Y = AK 0.5 N 0.5. (a) Find an expression for the marginal product of labour. (b) Hence find labour demand as a function of the real wage, w and productivity A. (c) Meanwhile, suppose that labour supply of workers is described by N S = 0.5w(1 t), where t is the tax rate. Find the equilibrium real wage and equilibrium employment (N) if A = 1.0 and t = 0.3. (d) Find the effects on the real wage and employment of a productivity improvement, A = 1.1. (e) Find the effects on the real wage and employment of a tax cut to t = 0.27 ( a ten percent tax cut ) with A =

3 Exercise A. Answers This assignment is marked out of This question is worth 6 marks. (a) Levels: Ontario Québec Year GDP population GDP/pop GDP population GDP/pop Note: GDP per capita is measured in thousands of current dollars. (b) Growth rates: Ontario Québec Year GDP/pop GDP Pop. GDP/pop GDP Pop % The second column shows the growth rates of GDP per capita for Ontario (as percentages) while the fifth column shows the values for Québec. (c) Information to answer this question also is shown in the previous table. Notice that the growth rates of GDP per capita are approximately equal to the growth rates of GDP minus the growth rates of population; the differences arise because of rounding and because that formula is an approximation. During these three years, Ontario had higher growth rates of GDP per capita than did Québec, especially in These differences occurred even though Ontario s population growth rate was 1 percentage point above Québec s. 3

4 2. This question is worth 5 marks. (a) The data you find may depend on the date of retrieval, for some data may be revised as those from 2001Q2 are added. Here are the data we found in August: Year Quarter Real GDP Inventory investment (b) Clearly inventory investment as a share of GDP fell sharply from the first quarter of 2000 to the first quarter of But notice that the start of 1999 also saw a low number (which was negative). To put this decline in perspective, one could look at (i) other countries and (ii) previous recessions. But, even finding that this decline was unusual would not mean that this was the real cause of the slowdown. Investment is endogenous. 4

5 3. This question is worth 9 marks. (a) The national saving rate is 13.9%. (b) Private saving as a share of GDP is 11.9% (Remember also that this is different from the private or personal saving rate.) (c) Initially I exceeds S pvt by 4.4 percentage points. The forecaster is implicitly predicting that this gap will narrow to 3.5 percentage points. We cannot tell whether this involves a fall in the investment share or a rise in the share of private saving. 5

6 4. This question is worth 7 marks. (a) r at = i(1 τ) π Notice that taxes are paid on nominal interest income, so to calculate the after-tax real return, subtract inflation from the after-tax nominal return. (b) The issuer of debt promises that the left-hand side does not change. So if π rises by 1, for example, then i must rise by 1/(1 τ) = In general, there would be larger swings in this nominal interest rate than in inflation. (Conversely, that means that if other bonds have nominal interest rates that do not have such amplified swings then their real, after-tax returns must vary when inflation does.) 6

7 5.This question is worth 11 marks. (a) These figures give A = in 1975 and A = in 1995, for a growth of 62 %. You should also be aware that if you calculate the A growth rate using the formula: Y Y = A A + α K K K + α N you will get an erroneous answer. The reason is that this formula is an approximation that works well for small changes in K N K or/and N which is not the case here. In fact we have that K K = 256% here which is too large. Fortunately for the people that used this approximation to find their answer, they will not be penalized this time as some TA s did not provide this precise answer when they were asked about that issue. Nevertheless you can be well advised that this will not be true for the next assingment or the Midterm. Beware! N N (b) Output per worker is 6.66 in 1975 and in 1995 for growth of 114%. (c) The upward revision in the input growth leads to downward revisions in the estimates of productivity growth. Output per worker in 1995 now is 12, and so growth in output per worker is 80%. And A = in 1995, so that TFP growth over the twenty-year period is 43.4%. (d) For growth over twenty years of a percent, we want the implicit, percentage growth per year, denoted b: The formula is: ( b ) 20 ( a ) 1 + = which we then solve for b. Of course, if we had annual data on the outputs and inputs, we could construct the series of annual productivity growth rates, which would vary over time. 7

8 6.This question is worth 12 marks. (a) The marginal product of labour is MPN = 7.071AN 0.5 (b) The labour demand curve is given by: w = 7.071AN 0.5 or N = 50 A2 w 2 (c) w = 5.23 and N = (d) Now w = 5.57 and N = The rise in TFP raises both real wages and employment. (e) Now we have w = and N = The supply curve has shifted out. (This is supply-side economics.) 8