Homework ch 20 ECO 201: Principles of Macroeconomics Questions 5 and 6 Exercises 2, 3, 8, and 9 (use lots of graphs for 9 – the Additional Questions should be helpful) Additional Questions See the Workbook below Note for Question 5 Notice that Investment is basically the “demand for saving,” while Saving is “the supply of saving.” Note for Question 6 Answer this question both with words and with a graph. Note for Problem 2 A flow is something that is measured over a period of time (say, a entire year). For example, your income is a flow ($50 per week). If I ask you, “how much are you earning at this very second?” the question wouldn’t make sense to you. But if I ask you, “how much are you earning this year?” you can say, “$2500.” A stock is something that is measured at a point in time. For example, your student debt is a stock ($10,000). If I ask you, “how much do you owe at this very second?” the question makes a lot of sense: $10,000. But if I ask you, “how much are you owing during the year?” you’d hem-and-haw and say that on January it was so much and then in April that much and then in December this other much. The change in a stock is a flow; a stock is the accumulation of past flows. For the questions, ask yourself: is this a flow, like income, or a stock, like debt?Note for Problem 3 In this problem you want to ask yourself whether Ellie and Vince 1. want to put away some money for a predictable event that will happen in the future (such as retirement or children’s education); 2. want to put away some money for an unpredictable but possible event that will cost a lot (such as an accident); 3. want to give to someone else (children, charities, etc.) Notice that the amount of saving might be affected by how much wealth they already have (more wealth would make more saving less necessary) and by the interest rate (higher interest rates make saving more attractive because wealth can be accumulated faster. Note for Problem 8 Here is part (a) and part (b) solved for you: Number of screens Marginal product Value of marginal product 1 40,000 $80,000 2 35,000 70,000 3 30,000 60,000 4 25,000 50,000 5 20,000 40,000 VMP is calculated with a per-ticket price of $2. The marginal products decline as screens are added, illustrating diminishing returns to capital. b. The interest cost of each screen is 5.5%*$1,000,000, or $55,000. There are no other costs mentioned. The value of marginal product exceeds $55,000 for 3 screens but not 4. So 3 screens should be built. If the interest rate is Interest payments will be 5.5% $55,000 7.5% 75,000 10.0% 100,000 Note for Problem 9 Here is part (a) and part (b) solved for you. • DRAW GRAPHS • LABEL THE AXES • Say what happens to EQUILIBIRUM SAVING and INVESTMENT and to the INTEREST RATE a. The investment tax credit effectively lowers the price of new capital goods to the firm by 10%. Firms’ willingness to invest increases, raising the demandfor saving (I). The real interest rate, investment, and national saving rise as the demand for saving (I) curve shifts to the right. r S I’ I I, S b. Increased public saving raises national saving. The supply of saving (S) curve shifts right. The real interest rate falls, national saving and investment rise. r S S’ I I, S Additional Questions Workbook Solved for you: 1. Identify the following equations: S = 1000 + 2000 r I = 1500 – 3000 r 2. Explain, giving the economic intuition, the signs of the slope of each line. That is, why is S positively related to r but I is negatively related to r? 3. Solve this system of equations and find what are national saving, domestic investment, and the real interest rate in equilibrium? 4. Suppose a rise in the government deficit reduces national saving at every level of the interest rate by 500. How do the equilibrium values of saving, domestic investment, and the real interest rate change? 5. Suppose that a foreign war depresses business confidence, reducing investment at every level of the interest rate, so that now I = 1250 – 3000 r. Find the new equilibrium values of saving, domestic investment, and the real interest rate.Solve on your own: 6. Suppose that a decline in consumer confidence reduces consumption, so that Private Saving rises at every level of the interest rate. This means that the intercept of the S equation is now larger by 500. Calculate the equilibrium values of saving, domestic investment, and the real interest rate. 7. Suppose that a discovery of natural resources expand investment opportunities at every level of the interest rate, so that now I = 1750 – 3000 r. Find the new equilibrium values of saving, domestic investment, and the real interest rate. Solved Problems 1. The equations are, in turn S = 1000 + 2000 r Supply of National Savings I = 1500 – 3000 r Demand for Savings (demand for investment goods, financed with savings) 2. Explain, giving the economic intuition, the signs of the slope of each line. That is, why is S positively related to r but I is negatively related to r? You can tell what the slope of the line is by looking at the sign of the coefficient next to the variable. The slope of the Supply of National Savings curve is positive because National Savings are also attracted by higher real rates of return, given the opportunity cost (that is, consumption today). Domestic savers also desire to maximize the value of their wealth, and they are only willing to give up current consumption if they obtain high levels of future consumption in return. The slope of the Demand for Savings (Investment) curve is negative because firms compare the Value of the Marginal Product of additional units of capital with the interest rates. Because of diminishing returns, additional units of capital have lower VMPs. If real interest rates rise, only the first few units of capital will be profitable (so the quantity of investment will be low); if real interest rates fall, many units of capital will be profitable, and the quantity of investment will rise.3. Solve this system of equations and find what are national saving, domestic investment, and the real interest rate in equilibrium? To obtain the answer from this system of equations, first we need to make sure that we have the same number of equations as unknowns. At first it looks like we have 3