Midterm Examination Number 1 February 19, 1996

Transcription

1 Economics 200 Macroeconomic Theory Midterm Examination Number 1 February 19, 1996 You have 1 hour to complete this exam. Answer any four questions you wish. 1. Suppose that an increase in consumer confidence raises consumer's expecations of future income and thus the amount that they wish to consume today. How would this affect investment and the real interest rate. 2. Is the US saving rate too low? By what standard? Would a rise in the US saving rate permanently increase the rate of economic growth as measured by the annual percentage increase in per capita GDP? What are the costs and benefits of a rise in the US saving rate? 3. The chart below plots average annual growth rates over the period 1960 to 1985 against GDP per person in What are the implications of this data for the convergence hypothesis? Growth and Initial GDP per Person Average annual growth rate 1960 to GDP per person in 1960

2 4. Consider an economy that obeys the Solow growth model (with no technological progress) and has the aggregate production function 250. (a) Show that the per capita production function is (b) Suppose that the economy has a saving rate of.2 and that the rates of population growth and depreciation are 1% and 4% respectively. Give the equation describing how changes over time. (c) Find the steady-state amounts of capital and output per person. 5. Consider an economy whose (per-capita) production function is where and are output and capital per worker respectively and is a positive constant. Use the law of motion for from the Solow model (ignoring technological progress) to show that, in this economy, a rise in the saving rate will permanently increase the rate of growth. Compare and contrast (as appropriate) this with the usual Solow model that we studied in class. 6. During the decade from January 1981 to December 1990, the average annual rate of growth of GDP was 2.3%. Over the same period the labor force grew at an average annual rate of 1.0% and the capital stock at an average annual rate of 2.0%. If capital's share of output was an average 30% during this period, decompose the growth in GDP into the portions due to growth in total factor productivity, the capital stock and the labor force. Be careful to state any assumptions that you make.

3 Economics 200 Macroeconomic Theory Solutions to Midterm Examination Number 1 February 19, The supply of loanable funds is given by. For any given value of a rise in consumption for each level of disposable income reduces saving. Thus the supply of loanable fund shifts to the left as shown below. The demand for loanable funds,, does not change. The new equilibrium has a higher real interest rate and lower investment. 2. Compared to the Golden Rule saving rate, which is equal to capital's share of output (about 30% for the US), the current average US saving rate of about 17.5% is too low. In the Solow model a rise in the saving rate produces a rise in the growth rate only during the transition to the new steady state. Once that point is reached the growth rate of per capita GDP is again the same as the rate of technological progress. Raising the saving rate would put the economy on a transition path to a steady state with higher per capita consumption than at present. The cost is a lower level of per capita consumption now because a higher saving rate implies lower consumption until the higher savings result in a sufficiently large increase in the capital stock to give higher consumption.

4 3. The convergence hypothesis is the claim that, eventually, all countries will have the same level of per capita income. It is motivated by the observation that, in the Solow growth model, the steady state level of income per capita is independent of the starting level. The implication for cross-country data on levels of per capita GDP and subsequent growth rates is that the two ought to be negatively related. The poor countries need to grow faster than the rich if they are to catch up. This is illustrated in the diagram over. Thus, a plot of the average growth rate over some time period against level of per capita GDP at the beginning of the period ought to display a negative relationship between these two variables. The data in the chart are inconsistent with this prediction and thus with the convergence hypothesis. If, however, we were to look at countries that are sufficiently similar such as those in the OECD or at the states of the US we find that the data support this implication of the convergence hypothesis (a) (b) We have.2, 01 and.04. Given that the growth rate of the 250 capital stock is given by we have (c) In the steady state 0 so Thus, the steady-state values of capital and output per person are and 2500 respectively

5 5. The law of motion for the per capita capital stock can be written as. In this problem so the law of motion becomes. This model is shown in the chart below. An increase in the saving rate from to shifts the line up and permanently increases the growth rate. The key difference between this model and the standard Solow model is the absense of diminishing returns to capital which drive the economy to a steady state as the rising capital stock brings constant increments to depreciation but declining increments to output and thus gross investment. In the case at hand, growth continues unabated as the capital stock rises. 6. Suppose that the aggregate production function is. Assuming that is constant returns to scale and that factors are paid their marginal products (competition) the growth rate of GDP can be decomposed as where is capital's share of output We measure growth in total factor productivity using the Solow residual computed as. Thus, of the 2.3 percent average growth in GDP, 1.0 percent was due to growth in total factor productivity (technological progress),.6 percent (.3 2.0) was due to growth in the capital stock, and.7 percent (.7 1.0) was due to growth in the labor force.

6 Economics 200 Macroeconomic Theory Midterm Examination Number 2 April 8, 1996 You have one hour to complete any four of the six questions below. Do not attempt to write on both sides of the page at the same time. 1. Consider the chart below. The "inflation differential" plotted on the horizontal axis is the indicated country's average inflation rate over the period 1970 to 1991 less that in the United States. The "percentage change in the nominal exchange rate" is the average annual percentage change in the country's exchange rate (measured as units of that country's currency per US$) over the same period. Describe the phenomenon you observe in this chart and use a theory or model to explain it. Note that, the exchange rate as defined here is the inverse of that defined in class so that if a currency falls in value relative to the US$ the exchange rate rises. In other words, in class we defined exchange rates from the US point of view (with the US as the domestic country) as number of units of foreign currency per US$ (that is, per unit of the domestic currency). Here we are traeting the US as the foreign country so the vertical axis shows % where is the nominal exchange rate defined as number of units of foreign currency per unit of domestic currency. 2. Why are the fiscal and trade deficits sometimes referred to as twins? 3. Why does the aggregate demand curve slope downward?

7 4. What is the classical dichotomy"? Describe a model that does not exhibit this property. 5. In a newspaper article in the early 1980s, a reporter wrote Comment on the reporter's claim. A new recession is feared because higher Pentagon spending is raising interest rates. Those higher rates are discouraging housing purchases and plant and equipment investment. 6. Suppose that US firms are given much greater access to Chinese and Japanese markets. Analyze the long-run effects on the US GDP, trade balance and real exchange rate.

8 In an announcement more important to academics than the apprehension of the Unabomber, Professor Paul Johnson of Vassar College today revealed the answers to the second Economics 200 midterm. chart. Note however, that the observed relationship is not exactly is predicted as it would be if all of the points were to lie on the line added to the chart below. Professor Johnson In particular, note that all but one country (Canada) lie below the line implying that for most of them %. Why this is so is one of the topics discussed in Economics Professor Johnson revealed that the answers were: 1. The chart shows that there is a strong tendency for the currencies of countries with average inflation rates greater (smaller) than that in the US to depreciate (appreciate) relative to the US$. Treating, for example, Italy as the domestic country we know that the percentage changes in the exchange rates (nominal and real) and the rates of inflation in Italy and the US (the foreign country here) % % % % where is measured in units of US$ per Lira. So, if the cross-country variation in % is small relative to that in the other terms, we have % % % which can be written as % % %. This positive relationship between % and % % is observed in the 2. Beginning with the identities and we can write. Thus. Given that, particularly over long periods of time, and move together, much of the variation in comes from that in So, if there is a large fiscal deficit there will also tend to be a large current account deficit. This relationship, and its graphic illustration during the last 15 years or so, has prompted some to refer to the deficits as twins. 1 You were not required to observe this phenomenon nor explain it to obtain full credit for this question. I just could not resist the opportunity to point this out and advertise one of the other classes that I teach! Page 1

9 Economics News April 8, The aggregate demand curve slopes downward because, holding all else constant, a higher price level implies a lower level of real balances, shifting the LM curve to the left. In the diagram below the price level is greater than so the LM curve associated with lies to the left of that associated with. The new short-run equilibrium point has a higher interest rate (and thus lower investment) and a lower level of GDP demanded. Thus, all else constant, there is a negative relationship between the price level and the quantity of GDP demanded. In other words we have found two points and ) on the AD curve as shown. This is not to imply that a higher price level reduces GDP but only that, all else constant, a higher price level implies a reduction in the aggregate quantity of goods and services demanded. 4. A model of the economy exhibits the classical dichotomy when the real variables (quantities and relative prices) can be determined without reference to the nominal variables (for example, the price level and the money supply). One way to break the dichotomy is to postulate that consumption depends on the level of real balances,, and write the consumption function as. The idea is that real balances are a form of wealth and higher wealth increases consumption at each level of disposable income. Let the demand for real balances be given by where is the nominal interest rate which can be written as Page 2

10 Economics News April 8, 1996, where is the expected inflation rate. Assume that expected inflation is given by, where is the rate of growth of the money supply. Assembling all of this under the assumption that the demand for and supply of real balances are equal, we can write the consumption function as. The supply of loanable funds is now given by. We discovered in problem sets 4 and 5 that, for each value of, a rise in increases the nominal interest rate, reducing the demand for real balances and hence the quantity of real balances that are held. This reduction results in lower consumption and hence higher saving implying a rightward shift in the supply of loanable funds curve. This shift in the savings function moves the market to a new equilibrium with a lower real interest rate and higher saving and investment. The fall in the real interest rate given a rise in the rate of growth of the money supply violates the classical dichotomy. the amount of crowding out ( ) equals the fall in investment times the multiplier. However, for the reporter's fear of a recession to be well founded, the reduction in investment would have to exceed the rise in government spending As the reporter is concerned about a recession, a model of the short-run behavior of the economy is appropriate. Consider the effects of a rise in government spending in the IS-LM model illustrated below. The rise shifts the IS curve to the right by an amount equal to the rise times the autonomous spending multiplier (the length of the arrow). GDP does not, however, increase by this amount as that would imply that the economy was off the LM curve with the demand for real balances exceeding the supply. To keep the money market in equilibrium interest rates must rise as the reporter suggests and this will indeed reduce investment. The result is that GDP increases from to rather than to. Note that 2 This would require a negatively sloped LM curve. To see this, draw an IS-LM diagram with a negatively sloped LM curve steeper than the IS curve and then increase government spending. What would give such an LM curve? Page 3

11 Economics News April 8, The appropriate model is that of a large open economy. The greater access to Chinese and Japanese markets increases exports for each value of the real exchange rate and so shifts the function to the right. as shown below. Nothing in the loanable funds market changes so NCO is unchanged. With the new function this means that the real exchange rate must rise. The intuition is that the relative price of domestic goods and services rises as the demand for them increases. Domestic GDP is unchanged because it depends on the available quantities of capital and labor and the level of technology, none of which have changed. Student reaction to the answers is unknown at this time. I hope that these answers are not news, said Johnson, but we will have to wait until I grade the exam papers before we know for sure. Page 4

12 Economics 200 Macroeconomic Theory Final Examination May 13, 1996 You have two hours to complete this exam. Answer any 8 questions. 1. Consider the Cobb-Douglas production function where all symbols have their standard meanings. Let and. (a) Show that. (b) Using the production function in (a), show that, in the Solow growth model with no technological progress, the steady-state level of is given by. (c) Show that the golden-rule level of in this economy is given by given by. HINT: For the production function,. (d) Use the results in (b) and (c) to conclude that the golden rule saving rate is. Interpret this result. 2. While relaxing this summer you pick up a copy of the Economist. Among the letters to the editor you notice an item criticizing a recent report on the closed economy of Ferme in which it was claimed that investment as a fraction of GDP rose from 10% during the 1970s to 15% during the 1980s while the real interest rate rose from 2.5% to 4%. The writer of the letter states that this claim is obviously absurd as everybody knows that investment falls when real interest rates rise. What is your view? 3. Why does the aggregate demand curve slope downward? 4. Consider an economy with the Phillips curve (a) What is the natural rate of unemployment for this economy? (b) Graph the short-run relationship between inflation and unemployment. (c) What unemployment rate is required to reduce inflation by 1 percentage point? (d) If Okun's Law is 2.06, what is the sacrifice ratio? 5. Suppose that during the summer you are retained as a consultant by the central bank of a small open economy that places no restrictions on the flow of capital across its borders. The central bank is considering a change in the exchange rate regime from its current fixed exchange rate to a freely floating exchange rate. You are told that most of the shocks in the economy originate in the goods market and that the citizens value stability in the level of GDP. Would you advise for or against the change? Why? 6. Analyze the long-run effects on the US GDP, real interest rate, real exchange rate and current account balance of an increase in taxes.

13 7. Analyze the short-run effects of a rise in the world real interest rate on the GDP, real interest rate, real exchange rate and current account balance of a small open economy with a floating exchange rate and perfect capital mobility. 8. Most of our discussions of the IS LM model assumed that expected inflation was zero so the real and nominal interest rates were equal. In this question we will modify the model to allow for nonzero, but exogenous, expected inflation. One way to do this is to write the investment and money demand function as and respectively, where is the expected inflation rate. The IS and LM functions become and respectively. Your task is to use a diagram and careful explanation to indicate the short-run effects on,, and of a rise in beginning from and a position of full employment,. Note that even when we continue to assume that is fixed in the short run. HINT: Put on the vertical axis in the IS LM diagram. 9. What are the implications of the convergence hypothesis for cross-country or crossregion data on levels of per capita GDP and growth rates? What evidence is there supporting or rejecting these implications? 10. The following chart plots decade average inflation rates in the United States for the 1870s through the 1980s against the corresponding money growth rates. Describe the relationship between these two variables and use a model to explain that relationship.