Problem Set #3 (15 points possible accounting for 3% of course grade) Due in hard copy at beginning of lecture on Wednesday, March

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1 Department of Economics M. Doell California State University, Sacramento Spring 2011 Intermediate Macroeconomics Economics 100A Problem Set #3 (15 points possible accounting for 3% of course grade) Due in hard copy at beginning of lecture on Wednesday, March Please follo all the instructions, or your problem set ill receive no points. All ansers must be on the anser sheet or attached sheets as instructed. Turn in only the anser sheets and attachments. Write your name at the top of every attached page and staple all pages together into one set ith the pages in the proper order. Do not turn in this sheet of questions. Problem sets are due at the beginning of lecture and ill not be accepted late. Your submitted ork must be your on. Problem sets that are identical (in hole or in substantial part) to another student's problem set ill receive a zero. As you ill notice, the point value for each individual question or part of a question is relatively small. This being the case and given the large number of problem sets I must grade, there ill be no partial credit. I ill, hoever, grade somehat more leniently than on an exam and ill aard full credit for any single anser that indicates to me that you mostly get it. This being the case though, you must be sure to compare your ansers to those on the anser key. Don t assume that your anser is 100% correct and that a similar anser to a similar question on an exam ill earn you full credit just because you received full credit on the problem set. Problem sets should NOT be left in my Economics Department mailbox or under my office door. I am not responsible for problem sets turned in any ay other than to me at the beginning of lecture. No electronic submissions ill be accepted. 1. (2 points total) Suppose production is represented by Y = AK here the variables have the usual meanings as e have used them in class and output is measured in trillions of dollars hile labor is measured in trillions of hours. a. ( ½ point) Find the marginal product of labor and express it in terms of output and labor only. (You must sho your ork to receive credit.) b. ( ½ point) Suppose that output is $75 trillion. Find the equilibrium number of labor hours if the age rate is $10 per hour. c. (1 point) Suppose the actual age is $15 per hour, but the number of labor hours is as you found in part b. Draing on our class discussion and your reading, explain ho this could be. Note: A superficial and/or vacuous anser just ill not be sufficient here. 2. (2 points ½ point each part) Suppose Susanna can ork any number of hours she ants to and that she currently orks eight hours per day and consumes eight hours per day of leisure. Also, assume that her hourly age is $25 per hour. a. Using a diagram such as that in lecture, dra Susanna s budget constraint ith all other goods on the vertical axis and leisure on the horizontal axis. b. Dra a representative indifference curve and illustrate Susanna s utility maximizing location on her budget constraint. Be sure to label everything and to indicate her current level of consumption of all other goods. (Note: You should initially ork this problem on scratch paper as this part and the next part ill require rather precisely dran indifference curves.) c. Suppose that Susanna receives a pay raise and is no paid $30 per hour. Also suppose that Susanna continues to ork eight hours a day. Illustrate this on your diagram from part b, being sure to dra the ne budget constraint and a ne indifference curve shoing Susanna s ne utility maximizing position and ne consumption of all other goods.

2 d. Based on the scenario in part c, hat can you say about the substitution and income effects as they affect Susanna s utility maximizing choice hen faced ith a age increase? Be specific and explain as fully as you can. 3. (4 points total) Suppose a small open economy represented by the folloing equations here C represents consumption, Y represents output, T represents taxes, G represents government purchases, I represents investment and r represents the orld interest rate (expressed in decimal form) and here all values are in billions of dollars: C = r ( Y T ) Y = 19 T = 6 I = 6 100r G = 6 a. (1- ¼ points)find the values for national saving, net exports and the change in net foreign assets for values of r of 2%, 3%, 4%, 5% and 6%. Enter the values in the table on the anser sheet. b. ( ½ point) Derive a saving function and graph it. Be sure to clearly label the axes and the saving function. c. ( ½ point) Graph the investment function. Be sure it is labeled. d. On your graph, label or illustrate the folloing: i. ( ¼ point) the orld interest rate for hich net exports ould be equal to zero ii. ( ¼ point) the net exports and capital flo hen the orld interest rate is 3% iii. ( ¼ point) Is the net capital flo in the previous part an inflo or an outflo? 4. (5 points total) Consider a orld ith to large economies. We ill call these economies ome (you can think of this as the U.S.) and Foreign (hich you can think of as the rest of the orld). With all variables defined in the same manner as in the previous question, except ith the subscripts to represent ome and F to represent Foreign, these economies are defined as follos: ome Country C = r + 0.4( Y T ) Y = 1000 T = 200 I = r G = 275 Foreign Country C F = r + 0.4( YF TF ) Y F = 1500 T F = 300 I = r G = 300 F F Note: For this question you must sho all of your ork. Complete your ork on a separate sheet and attach behind the last page of the anser sheet. a. Find the values of the folloing: i. ( ½ point) the equilibrium orld interest rate, r ii. (1 point) equilibrium values of consumption, national saving, investment and net exports for ome iii. (1 point) equilibrium values of consumption, national saving, investment and net exports for Foreign b. (1 ¼ point) Suppose that in ome the government purchases increase by 50 to 325 and that taxes also increase by 50 in order to keep the deficit from groing. Repeat parts a.i, a.ii and a.iii from above.

3 c. (1 ¼ points) Explain your results. Tell me hat is driving them. In other ords, do net exports change even though the deficit doesn t? Why do e see the result e do? Address this both in terms of the math or equations and also in terms of the underlying economic theory. This should be a thoughtful anser that demonstrates hat I expect ill be your deep understanding of the model at hand. A superficial anser ill be absolutely unacceptable and ill be marked accordingly. 5. (1 point) Suppose the money supply M has been groing at 10% per year, and nominal GDP PY has been groing at 20% per year. The data are as follos (in billions of dollars): M PY 1,000 1,200 1,440 Calculate velocity in each year. o fast is velocity groing? 6. (1 point total ¼ point each part) Anser the folloing four parts. Each part is independent of the others. a. Calculate hat happens to nominal GDP if velocity remains constant at 5 and the money supply increases from $200 billion to $300 billion. b. What happens to nominal GDP if the money supply gros by 20% but velocity decreases by 30%? c. If credit cards ere made illegal by congressional action, hat ould happen to velocity? Explain. d. If velocity and aggregate output ere reasonably constant (as the classical economists believed) hat happens to the price level hen the money supply increases from $1 trillion to $4 trillion?

4 Spring 2011 Economics 100A-01 Anser Sheet for Problem Set #2 Name: Solutions Write your ansers in the space indicated. Possible points for each anser are given in parentheses. Ansers ill be graded only hen placed in the space provided. You must rite legibly or I ill not grade your ansers. 1.a.i. (1) Sho your ork here and enter final result belo. You are given the production fn. Y = AK Take the first derivative ith respect to labor: Y = 0.65AK = 0.65AK To simplify, multiply by /: AK Y 0.65AK = 0.65 = 0.65 = MP MP = Y b. ( ½ ): Equilibrium abor ours: trillion

5 1.c. (1) The age could be above equilibrium due to rigid or sticky ages. Sticky ages are ages that fail to adjust quickly so as to clear the labor market. Sticky ages are explained primarily by collective bargaining or union contracts and efficiency age arguments. See chapter 20 of the textbook for additional discussion of these topics. 2.a, 2.b and 2.c (1/2 point each part) AOG $480 $400 $240 U 2 $200 U 1 8 eisure

6 2.d. ( ½ ) The income and substitution effects exactly offset each other. The income effect by itself ould cause Susana to consume more leisure as ell as more of all other goods. The substitution effect ould cause her to consume less leisure as it is no more expensive relative to all other goods. 3.a. (1-¼ ) r = 2% r = 3% r = 4% r = 5% r = 6% National Saving Net Exports Change in Net Foreign Assets b.and 3.c ( ½ point. each) and 3.d.i and 3.d.ii ( ¼ point each) r NX S 3% r for hich NX = 0 S, I I

7 3.d.iii ( ¼) The net capital flo is a(n) out flo 4.a.i ( ½ ) R = 0.05 = 5% 4.a.ii and 4.a.iii ( ¼ point each part) County Consumption National Saving Investment Net Exports ome Foreign b ( ¼ ) R =0.08 = 8% ( 1/8 each part) County Consumption National Saving Investment Net Exports ome Foreign c. (1-¼ ) Net exports do change. They decrease. This occurs because national saving is reduced due to the fact that C + G increases. This is because the increase in G (50) is larger than the decrease in C (mpc x -50 = -20)

8 5. ( ¼ point each part) Year Velocity Groth rate of velocity is: Approx 9.1% 6.a ( ¼ ) The money supply has gron by 50% so given constant velocity, nominal GDP ill gro by 50% as ell. 6.b ( ¼ ) +20%-30% = -20%. Nominal GDP declines by 10%. 6.c ( ¼ ) Velocity ould decrease as in the absence of credit cards e ould need larger money balances to carry out our transactions. 6.d ( ¼ ) It ould increase four-fold as ell.