1. Suppose that the government decides to reduce expenditures. In the basic model used in Lecture 6, determine its effects on aggregate output, consumption, employment, and the real wage, and explain your results. 2. Suppose that there is a natural disaster that destroys part of the nation's capital stock. (a) In the basic model used in Lecture 6, determine the effects on aggregate output, con- sumption, employment, and the real wage, with reference to income and substitution effects, and explain your results. (b) Do you think that changes in the capital stock are a likely cause of business cycles? Explain, with reference to your answer in part (a) and the key business cycle facts described in Lecture 3. 3. Suppose that government spending makes private firms more productive; for example, gov-ernment spending on roads and bridges lowers the cost of transportation. This means that there will now be two effects of government spending, the first being the effects discussed in this lecture of an increase in G and the second being similar to the effects of an increase in the nation's capital stock, K. (a) Show that an increase in government spending that is productive in this fashion could increase welfare for the representative consumer. (b) Show that the equilibrium effects on consumption and hours worked of an increase in government spending of this type are ambiguous, but that output increases. You will need to consider income and substitution effects to show this. 4. In the one-period model, education can be represented as time spent by the representative consumer that is neither leisure nor time applied to producing output. Whht the economy gains in the future is that the productivity level z will increase. (a) Using the one-period model, show what effects additional education has in the present on consumption, leisure, employment, aggregate output, and the real wage. (b) Similarly, show the effects the additional education that people acquire today will have in the future on consumption, leisure, employment, aggregate output, and the real wage. (c) What does your analysis in parts (a) and (b) have to say about the tradeoffs society makes between the present and the future in investing in education. 5. Consider the following economy. The representative consumer's preference is described by U(C, I) = log(C) + a log(l). The representative firm produces output by combining capital and labor input: Y =zF(K,N*d)=zKN"d. The government expenditure is 0. For simplicity, assume thatz=1,a=2,K=1,G=0,h= 24. Solve for the social planner's problem. Specifically, solve for optimal employment, leisure, consumption, output, and the implied wage and profit