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Consider the full version of the Solow model with both population growth and technology: Yt = F(Kt,LtEt). We will extend this version of Solow to also explicitly include the government. The national income accounts identity becomes: Yt = Ct + It + Gt where Gt is government spending in period t. In order to fund its spending the government collects a tax Tt. Suppose for simplicity that the government runs a balanced budget Gt = Tt and that the tax collected is a constant fraction of output: Gt = Tt = Yt. The remaining disposable income for households each period is (1 )Yt. As in Solow we still assume that households save/invest a constant fraction s of their (now disposable) income. The population growth rate is n, techonology grows at g, and the depreciation rate is . (a) Assume for now that there is only private and no public investment (i.e all government purchases are spent on consumer goods and none of Gt is used to invest in capital). Write down the standard system - the equations for output, consumption, investment, and the capital accumulation equation. Define: yt = Yt/EtLt,

kt = Kt/EtLt,

it = It/EtLt,

ct = Ct/EtLt,

gt = Gt/EtLt.

(b) Transform the model from part (a) in per- effective worker form and derive the steady-state equation for capital per effective worker. Draw a graph depicting the steady state.

(c) What is the effect of higher tax rate on the steady state? Show the effect on your graph and explain the intuition for your answer.

d) Now suppose that, in addition to the case in part (a), a fraction of Tt is also invested in the capital stock, i.e. public investment equals Tt = Yt. What is total investment equal to now? Similarly to part (b) derive the steady-state equation for capital per worker and depict your answer on a graph.

(e) Show that if is sufficiently high (i.e. you will need to find a specific threshold value), then the steady state capital per effective worker will increase as a result of higher taxation.

1. Unemployment is countercyclical, this means that when the GDP is __________, we should expect unemployment to be __________. a) in a boom, in a boom as well b) increasing, in a boom c) in a boom, below its trend d) In a burst, in a trough 2. If in 2011 the real GDP was $1000 and the nominal GDP was $1250, and in 2012, they were $1000 and $800, respectively, the GDP deflator in 2011 is ___________ the GDP deflator in 2012. a) greater than b) lesser than c) equal than d) it is impossible to determine with the information given 3. If Robinson lives only one period and its indifference curves between consumption and labor become steeper for any level of labor (graphing labor on the x-axis). Which of the following is not true. a) Robinson will works less and consumes less b) There was an upward proportional shift of the production function c) Robinson has to be more compensated with consumption for every extra unit of labor d) Robinson tastes over consumption and labor have change 4. The production function is ____________, but the marginal productivity of labor is ____________. a) positive, negative b) increasing, decreasing c) decreasing, increasing d) always constant, difficult to predict 5. Consider a production function y=f(l)=A*l 0.5+B. With an increase in B, and fixing the level of labor, the marginal productivity ______________ and the productivity, y/l, ____________. a) increases, does not change b) increases, increases c) does not change, decreases d) does not change, increases 6. Consider the infinite horizon budget constraint for a household, b0 (1+R)/p +y1+ y2/(1+R)+ y3/(1+R) 2 + .... = c1+ c2/(1+R)+..... In the aggregate economy, for some households, b0 >0, and ctyt for t > T, where T is some date in the future. While for other households, b0 <0, and ct>yt for t < T. What is the wealth effect for the aggregate economy if interest rate, R, increases? a. Positive b. Negative c. Zero d. Ambiguous 7. Consider the two period model in Chapter 3. Assume b0=b1=b2=0 at the beginning. Suppose there is a temporary downward shift in the schedule of the marginal product of labor today, while MPL tomorrow remains the same. This causes the level of consumption today _____, the level of work effort tomorrow_____, and the change of output today is _______ the change of consumption today. a. fall; rise ; larger than b. fall; rise: smaller than c. fall; rise; equal to d. fall; fall; equal to 8. An intertemporal substitution effect is caused by a a. change in the interest rate b. permanent, proportional shift to the production function c. temporary, proportional shift to the production function d. A and C 9. Consumption likely would increase the most when the production function shifts upward in a a. Permanent, parallel fashion b. Temporary, parallel fashion c. Permanent, proportional fashion d. Temporary, proportional fashion 10. Which of the following does not shift or rotate a person's budget line for consumption today and consumption tomorrow? a. An proportional upward shift of production function tomorrow b. A parallel downward shift of production function today c. An increase in the interest rate d. None of the above. 11. Suppose that desired saving declines at a given value of the interest rate. Also assume that consumption and leisure change "equally." Then the aggregate output ________, work effort ________, the interest rate ________, and the price level ________ a. Increases, increases, declines, declines b. Decreases, decreases, rises, rises c. Does not change, does not change, rises, rises d. Decreases, decreases, does not change, does not change 12. Consider a temporary parallel downward shift of the production function. How does the real demand for money, the interest rate, and the price level change? a. Increases, decreases, decreases b. Decreases, increases, increases c. Does not change, increase, does not change d. Not enough information to answer the question 13. According to the neutrality of money property, how does once-and-for-all increase in the aggregate quantity of money affect the interest rate R? a. R increases b. R decreases c. It does not affect R d. Not enough information to answer the question 14. Does Walras' Law hold when price of the commodity good is zero? a. No, because commodity market does not clear b. No, because money market does not clear c. Yes, if money market also clears d. Yes, if credit market also clears 15. Consider a temporary proportional downward shift of the production function. How does this change affect the work effort? a. The work effort decreases b. The work effort increases c. The work effort does not change d. Not enough information to answer the question 16. Which of the following decreases the real demand for money? a. A decrease in the aggregated price level. b. An increase in the time interval between successive trips to the bank c. A decrease in the nominal financial transaction fee. d. An increase in the number of shopping trips per period. 17. Which of the following increases the velocity of money? a. An increase in the number of shopping trips per period. b. A decrease in the real consumption expenditure. c. An increase in the time interval between successive trips to the bank. d. A decrease in interest rate. 18. A worker is paid an annual income of $12,000. He receives his paycheck once a month. His annual consumption expenditure is $12,000. He also shops once a month, immediately after receiving his paycheck. All else being equal, if his income and consumption expenditure increase by the same amount, his average money balance will ________. a. decrease b. increase c. remain the same d. We cannot tell given this information. 19. Assuming that household's money balance is constant over time, the presence of money in the budget constraint enables the average person to ________ consumption and ________ work effort. a. increase; no effect on b. increase; decrease c. decrease; no effect on d. no effect on; no effect on 20. Which of the following statements are true? I) The net wealth effect from money depends on the amount of money people presently possess relative to the amount they will demand in the future. II) Our theoretical model concludes that if the interest rate rises by 10 percent, the nominal demand for money falls by 10 percent. a. None of the statements are true. b. Statement I) is true. c. Statement II) is true. d. Statement I) and II) are true.