Economics 302 Spring 2005Homework #2Due February 16, 20051. Your liberal-activist roommate is plotting to bring down capitalist society. He/she claims that workers are being cheated out of compensation that is rightly theirs. He/she points to sizable profit announcements by large corporations as evidence that workers should be paid more. You decide (unwisely) to debate the issue from the standpoint of an academic economist. a. What common misconception about profit should you point out in your opening statement?Your roommate is likely thinking of accounting profits which are revenue minus operating costs (in our model this is labor cost). Accounting profits have not taken into account the fact that the owners of capital should be paid areturn.b. Explain how economists believe that wages are determined.Economist believe that real wages are equal to the marginal product of labor (MPL=w/p). This is the result of profit maximization. c. Show how if the aggregate production function is homogeneous of degree one (which is a reasonable long run assumption) that economic profit is zero rendering your roommate’s argument based upon profit weak. Be thorough in your explanation since your roommate is not easily convinced.If the production function is homogeneous of degree one it can be written asLMPLKMPKY .Knowing that the marginal products are equal to the real wage or real rental rate we can rewrite the above asLpwKprY .Multiplying through by the price of output we haveLwKrpY .The left hand side is the firm’s revenue and the right hand side is the firm’s costs. Since these two are equal, economic profits are zero.2. Suppose that the economy’s output is fixed by the amount of labor and capital present, the government balances its budget, the m.p.c. is 0.9 and NX = 0. Suppose the government increases its spending by 20% (taxes must increase to keep the budget balanced). a. Write the change in investment as a function of the initial level of government spending.1)2.0)(1.0( GI b. What must happen to the interest rate?As investment decreased, the interest rate must have risen. It is a good idea to check the loanable funds market to be sure that what occurs there is consistentwith a decrease in the interest rate. With our assumptions the savings equation becomesGYSavings 1.01.0 . So, as G increases savings decreases. Whensavings decreases the intersection of the savings curve and I(r) curve is at a higher interest rate and lower level of investment. c. In general, find an expression for the change in investment as a function ofthe change in government spending. GI  )1.0(d. Suppose now that when the government increases (or decreases) spending it leaves taxes unchanged. Find an expression for the change in investmentas a function of the change in government spending. GI e. Regardless of how the government finances increased spending what is theeffect on savings and the interest rate? Briefly explain.In the Classical model there is complete crowding out. That is, an increase in government spending reduced investment dollar for dollar. When the government is running a balanced budget the decrease in investment is smallerare the MPC is less than one. Consumption also decreases which means that investment does not need to change by the full amount. 3. For the years 1999 through 2004 collect data to calculate an estimate for the velocity of money. Nominal GDP can be used as an estimate of Outputice Pr.Data on the money stock can be found on the St. Louis Federal Reserve’s website located at http://research.stlouisfed.org/fred2/categories/24. Calculate the velocity using M1, M2, and M3 for each year. You will need to average the quarterly reports to get a yearly average of the money supply. a. Over the 5 years examined what is the trend in velocity? Yea r GDP M1 M2 M3 V(M1) V(M1)-M V(M2) V(M2)-M V(M3) V(M3)-M1999 9,268.40 1101.47 4525.873 6270.044 8.414571 -0.33964 2.04787 0.113449 1.478203 0.1402472000 9,817.00 1103.461 4801.405 6861.391 8.896557 0.142349 2.04461 0.110189 1.430759 0.0928032001 10,128.00 1136.99 5219.493 7643.641 8.90773 0.153522 1.940418 0.005997 1.325023 -0.012932002 10,487.00 1192.028 5614.811 8257.342 8.797615 0.043407 1.867739 -0.06668 1.270021 -0.067942003 11,004.00 1264.02 5998.417 8778.864 8.705558 -0.04865 1.834484 -0.09994 1.253465 -0.084492004 11,728.00 1332.24 6266.947 9232.705 8.803216 0.049009 1.871406 -0.06302 1.270267 -0.067698.754208 0.165838 1.934421 0.043453 1.337957 0.044785The velocity moves about depending on definition. It tends to be decreasing in theearly years with an upswing at the end. b. Which money aggregate is most consistent with a constant velocity?The final number in the columns labeled V(M )-M is the variance of the series. This is smallest for M2 but very close to M3’s variance. If you graphed the series they would look about the same.c. Having examined the data, is the assumption of a constant velocity justified? For M2 and M3 the movement around the mean is pretty small. I would say that constant velocity is an okay assumption at least in the short run.4. Again, record the price of the basket of goods you selected in the previous homework. Calculate a CPI like figure for the first period and this second period with the first measurement period being the base period. Recall that the CPI is a number around 100 and that it is based upon the price of the entire basket not individual