Economics 311 Money and Income First Exam-Spring 2002 Department of Economics College of Business and Economics California State University-Northridge Professor Kenneth Ng Monday, April 24, 2017

Question 1 Consider the production function in the table below. Use the graph below and graph the production function. Label points A, B, C, and D. A. Define the Marginal Product of Labor (MPL). B. What does the shape of the production function say about the MPL? Explain and demonstrate numerically using the numbers in the table. C. Draw the person’s indifference curve between consumption/output and work effort assuming that he chooses to work 2 hours. D. Show graphically and explain using the Marginal Rate of Substitution (MRS) and the MPL why the person will not voluntarily choose to work 3 hours. E. Suppose the production function experienced a proportionate improvement. Depict the change in hours worked and output. Does it matter if leisure is a normal or inferior good. Explain. Work Effort-L Output-F(L)=Y Point A 1 hour 10 units Point B 2 hours 19 units Point C 3 hours 24 units Point D 4 hours 30 units

Define the Marginal Product of Labor (MPL). B. What does the shape of the production function say about the MPL? Explain and demonstrate numerically using the numbers in the table. C. Draw the person’s indifference curve between consumption/output and work effort assuming that he chooses to work 2 hours. Output Marginal product of Labor:=Given the amount a person is working how much extra output will a person get if he works one more hour = slope of production function 30 24 A 19 10 1 2 3 4 Work Effort 50 104 104 104

Show graphically and explain using the Marginal Rate of Substitution (MRS) and the MPL why the person will not voluntarily choose to work 3 hours. Output At point B, the IC and PF are not tangent. The slope of the IC (MRS) and the slope of the PF (MPL) are not the same. Specifically, the MRS > MPL so the person values an hour of leisure more than the output he would get by giving up an hour of leisure and working. Therefore, he could make himself better off by consuming more leisure, i.e. working less, and producing less output. 30 B 24 A 19 10 1 2 3 4 Work Effort 50 104 104 104

Suppose the production function experienced a proportionate improvement. Depict the change in hours worked and output. Does it matter if leisure is a normal or inferior good. Explain. A proportionate improvement in the PF would rotate the PF from red to green. The total effect on work effort and output would be the sum of two effects- a wealth effect and a substitution effect. The S-Effect would be to increase work effort and output because the MPL has increased. The W-Effect would depend upon whether leisure is normal or inferior. If it is normal, the W-Effect would decrease work effort. If it was inferior, the W-Effect would be to increase work effort and output. Output 30 B 24 C A 19 10 1 2 3 4 Work Effort 50 104 104 104

Question 2 Consider a person who makes $50,000 this year and expects to make $100,000 next year and suppose the interest rate is 10%. Draw the person’s inter-temporal budget constraint and his indifference curve if he chooses to consume $75,000 this year. Label the vertical and horizontal intercepts and how much he would consume next year. Is the person borrowing or lending money? Explain. Suppose the person’s flow of income changed from $50,000 this year and $100,000 next year to $100,000 this year and $50,000 next year. Would this constitute a change in permanent income. Explain and depict on your graph. Suppose after the change in (B), the person continued to consume $75,000 this year. What would happen to the price of bonds and the interest rate? Explain and depict.

Future Consumption Present Consumption Consider a person who makes $50,000 this year and expects to make $100,000 next year and suppose the interest rate is 10%. Draw the person’s inter-temporal budget constraint and his indifference curve if he chooses to consume $75,000 this year. Label the vertical and horizontal intercepts and how much he would consume next year. Is the person borrowing or lending money? Explain. The original income flow ($50K this year and $100K next year) is point A. By borrowing and lending the household with this income flow over time can support consumption flows on the blue inter- budget constraint. The vertical intercept is given by: $100,000+ $50,000(1.1)=$155,000 The horizontal intercept is given by: $50,000+($100,000/1.1)=$140,909.09 Future Consumption Y=$155K Y=$100K A C C=$77, 500 B C=$72, 500 D Y=$50K Y=$50K $140,909 Present Consumption C=$75K 50 104 104 104

Future Consumption Present Consumption Suppose the person’s flow of income changed from $50,000 this year and $100,000 next year to $100,000 this year and $50,000 next year. Would this constitute a change in permanent income. Explain and depict on your graph. If the person income flow changed to $100K now and $50K next year, the household’s flow of income would be represented by point D. This would cause an increase in permanent income because money received now is more valuable than the same money received later. In the jargon of the inter-temporal budget constraint, it can support bigger flows of consumption over time. With the second flow of income, if we spend $75K today, we could save $25K today. If the interest rate is 10%, this will translate into $77,500 in the future (point C). Future Consumption Y=$155K Y=$100K A C C=$77, 500 B C=$72, 500 D Y=$50K C=$75K Y=$50K $140,909 Present Consumption 50 104 104 104

Future Consumption Present Consumption Suppose the person’s flow of income changed from $50,000 this year and $100,000 next year to $100,000 this year and $50,000 next year. Would this constitute a change in permanent income. Explain and depict on your graph. By moving from D to C, the household is saving money. This involves buying bonds. If all households bought bonds, the price of bonds will rise, and the interest rate will fall. This depicted as the rotation of the inter-temporal budget constraint to the blue dotted line. Future Consumption Y=$155K Y=$100K A C C=$77, 500 B C=$72, 500 D Y=$50K C=$75K Y=$50K $140,909 Present Consumption 50 104 104 104

Question 3 Use the 3-graph setup on the next page for your answer. Suppose the economy is in long run equilibrium with the production function the same now and in the future. Depict the economy. Suppose the production function is improves today but is not expected to change in the future. Show the effect on future and current output, work effort, and future and current consumption. What will happen to interest rates and bond prices explain? Will this effect the inter-temporal budget constraint? Explain and depict. Suppose expectations change and the current improvement in the production is expected to be permanent. Depict and explain the effect on future and current output, work effort, and future and current consumption. Which change in the production function will have a larger effect on output, work effort, and borrowing? Explain.

Suppose the production function is improves today but is not expected to change in the future. Show the effect on future and current output, work effort, and future and current consumption. The household will work more today and less in the future. By doing this they can maintain the same pattern of consumption over time with less total work effort. Now Future y1A y1 y2 y2A l2A l2 l1 l1A

Future Consumption A C2 = y2 C B y2A y1A C1 =y1 Present Consumption What will happen to interest rates and bond prices explain? Will this effect the inter-temporal budget constraint? Explain and depict. The household starts off at point A on the black inter-temporal budget constraint. When the current PF improves, the household will increase current work effort and reduce future work effort. The households income flow will be represented by point B. The household now evens out consumption by saving money today and getting the money saved plus interest in the future (point B to A). If all households did this the price of bonds would rise and interest rates would fall causing the inter-temporal budget constraint to rotate (blue line), leaving the household at point C. Future Consumption A C2 = y2 C B y2A y1A C1 =y1 Present Consumption 50 104 104 104

Suppose expectations change and the current improvement in the production is expected to be permanent. Depict and explain the effect on future and current output, work effort, and future and current consumption. Because the improvement in the PF is now viewed as permanent, there is no longer an incentive for the household to shift labor effort inter-temporally. Current work effort will decrease and future work effort will increase. Now Future y1A y1B y2B y1 y2 y2A l2A l2 l1 l1A

Future Consumption D A C2 = y2 C B y2A y1A C1 =y1 Present Consumption What will happen to interest rates and bond prices explain? Will this effect the inter-temporal budget constraint? Explain and depict. The permanent improvement if the PF causes permanent income to increase (the shift from black to green line. Because the improvement in the PF is permanent, households no longer lend money by buying bonds to even out their consumption over time so the slope of the inter-temporal budget constraint returns to its’ original slope. Because the future and present are the same, the household will choose a point like D on the new inter-temporal budget constraint. Future Consumption D C2 =y2B A C2 = y2 C B y2A y1A C1 =y1 Present Consumption C1= y2B 50 104 104 104

Summary Statistics. Without Homework With Homework Mean 38.4 51.4   Without Homework With Homework Mean 38.4 51.4 Standard Deviation 22.0 Students Taking Exam 41 Students Enrolled in Class 44 Grade Required Score Normalized Score Number Receiving Grade Percent Receiving Grade A 77 1.75 6 15% B 54 0.75 12 29% C 38 11 27% D 21 -0.75 7 17% F 5 12%

Administrative Details One Week Mandatory Cooling Off Period. Nothing concerning the exam, homework, scoring etc. will be discussed until next Thursday.