Professor Christina Romer SUGGESTED ANSWERS TO PROBLEM SET 5

Transcription

1 Economics 2 Spring 2016 Professor Christina Romer Professor David Romer SUGGESTED ANSWERS TO PROBLEM SET 5 1. The left-hand diagram below shows the situation when there is a negotiated real wage,, that is above the level where supply and demand are equal. At the negotiated wage, the supply of labor exceeds the demand. Employment is determined by the quantity of labor demanded at the negotiated real wage. There is unemployment equal to the difference between the quantity supplied and the quantity demanded at the negotiated wage. a. In general, a firm wants to hire workers up to the point where the marginal revenue product of labor equals the cost of employing a worker. In the absence of the mandated benefits, payroll taxes, and so on, the cost of employing a worker is just the wage, and so this condition is that the marginal revenue product of labor equals the wage. But if the firm is required to provide some benefit, the cost of employing a worker is the wage plus the cost of the benefit. Thus, a government requirement that firms provide employees with a new benefit, such as paid family leave, reduces labor demand. One way to see this is to note that another way to express the condition that the marginal revenue product of labor equals the wage plus the cost of the benefit (MRP L = w + b) is that the wage equals the marginal revenue product of labor minus the cost of the benefit (w = MRP L b). Thus, labor demand shifts down by the expected cost of the benefit. In the right-hand diagram below, it shifts down from to. Since employment is determined by the quantity of labor demanded at the negotiated real wage, employment falls (from N D1 to N D2 ). The benefit also makes working more attractive, and so it is likely to increase the quantity of labor supplied at a given wage; that is, it is likely to shift labor supply to the right. This shift would increase unemployment, but would have no impact on the real wage (which is determined by the negotiated wage) or employment (which is determined by the quantity of labor demanded at that wage). b S 2 N D1 N S1 N* Unemployment N D2 N D1 N S1 N s2 N* Unemployment 2

2 b. Increases in workers skills make them more productive, and so increase their marginal products. The higher marginal products mean that marginal revenue product is higher. (Since we are talking about the overall labor market, we do not have to worry about the possibility that the relative price of the goods the workers are producing will fall the workers are producing all the goods in the economy, so all prices move together.) As a result, the demand for labor shifts to the right, and so employment rises. The left-hand diagram below shows the normal case: the rise in labor demand (from to ) is not so large as to push the wage where supply and demand are equal above the negotiated wage. In this case, the wage is unchanged and unemployment falls but is not eliminated. The right-hand diagram shows the case of a very large increase in labor demand. In this case, the wage is now determined by the intersection of supply and demand. It is higher than the negotiated wage, and unemployment is eliminated. In both cases, employment rises (from N D1 to N D2 in the left-hand diagram, and from N D1 to N 2 in the right-hand diagram). 2 w 2 N D1 N D2 N S N* N D1 N S1 N 2 N* Unemployment 2 2. To analyze the behavior of the normal real interest rate and normal investment, we need to use the saving and investment diagram. Recall that firms purchase new capital goods up to the point where the present value of the stream of expected future MRP K s of capital equals the purchase price of capital. The problem states that firms become less optimistic about the future MRP K s. Thus, at a given interest rate, if they did not change the amount of investment they were doing, the present value of the stream of expected future MRP K s of capital would be less than the purchase price of capital. To restore the condition to equality, they need to purchase less capital, which will raise the MRP K s. That is, the investment demand curve shifts to the left (from to ). r* r 1 r 2 S*,I*

3 The diagram shows the effects of the change. The leftward shift of the investment demand curve causes us to move down the supply of saving curve. The normal real interest rate falls (from r 1 to r 2 ), and the quantity of investment falls (from to ) Planned aggregate expenditure () for a country is the total amount of spending people plan to do. It is the sum of consumption (C), the total amount consumers want to spend; planned investment (I P ), the amount firms plan to invest; government purchases (G); and net exports (NX), the amount foreigners want to buy from us minus the amount Americans want to buy abroad. Thus, = C + I P + G + NX. The expenditure line (also identified as ) shows how planned spending varies systematically with total output. It is upward sloping because consumption rises with total output (which is the same as total income). Its slope is less than one because people typically save at least part of every extra dollar of income they receive. In the short run, equilibrium output is determined by the intersection of the expenditure line and the 45-degree line. The 45-degree line represents the equilibrium condition that total output must equal total spending (Y = ) for the economy to be in balance. This line also captures the behavioral assumption that firms change output in response to changes in planned spending in the short run. a. Adding up the components of planned expenditure in this numerical example yields: = Y. Therefore, the equation for the expenditure line is: = Y. Y = (45-degree Line) (Expenditure Line) The expenditure line has an intercept of 800 and a slope of 0.6. The coefficient on output in the equation reflects the sensitivity of consumption to output. This coefficient is called the marginal propensity to consume (MPC). In this example, the MPC is 0.6, which means that if consumers get another dollar, they will spend 60 cents of it and save 40 cents. If you draw the expenditure line and the 45-degree line carefully, equilibrium output in the short run appears to be around. 800 Y b. The two equations that determine equilibrium output are Y = and = Y. Therefore, to solve for equilibrium output algebraically, all one does is substitute the second equation into the first. This yields: Y = Y (1 0.6)Y = 800 Y = 800/0.4 Y =

4 4 c. If planned investment increases to 500, this changes the equation for the expenditure line to: Y = = Y. Graphically, this is a shift up in the expenditure line by 200 at each level of Y (from 1 to 2). The new level of equilibrium output looks to be about 2500 in the graph Algebraically, the new level of equilibrium output is determined by calculating: Y = Y (1 0.6)Y = 1000 Y = 1000/0.4 Y = Y 1 Y 2 Y d. Output increases by more than the increase in planned investment because of the multiplier effect. The rise in planned investment increases output. The increase in output increases planned spending further because consumption depends on output. The further rise in planned spending increases output further, and so on. The algebraic formula for the multiplier is 1/(1 marginal propensity to consume). So, in this example the multiplier is 1/(1 0.6), which is 2.5. Notice, the size of the multiplier effect depends positively on the size of the marginal propensity to consume. This should make sense the larger the marginal propensity to consume, the greater the feedback effect of output on consumption. 4. The changes in G and T will have two opposite effects on the line. The reduction in G will make planned aggregate expenditure lower at a given level of Y. This will tend to shift the line down. The tax cut will make consumers disposable income, Y T, higher at a given level of Y. This will make consumption higher at a given level of Y, and so will tend to shift the line up. However, the two effects are not equal and opposite. G affects one-for-one: = C + I p + G + NX, so a $1 increase in G raises at a given Y by $1. But T does not affect one-for-one. If T falls by $1, C at a given Y rises by the MPC (which is less than 1) times the fall in taxes (which is $1); thus C rises by less than $1. That is, the negative effect on from the cut in G is larger than the positive effect from the cut in T. Thus, the line shifts down. As a result, as shown in the diagram, Y falls (from Y 1 to Y 2). 1 Y = 2 Y 2 Y 1 Y

5 5 5.a. False. If consumers decide to save more at a given level of income, this means that they are consuming less at a given level of income. This corresponds to a downward shift of the consumption function, which means that the line shifts down (from 1 to 2). As a result, output falls in the short run (from Y 1 to Y 2) rather than rises. Y = 1 2 Because the problem states that consumers save more at a given level of income, we know that the line must shift. If consumers also want to save more of each additional dollar of income they get, this Y 2 Y 1 Y would imply that the MPC has also gotten smaller (so the expenditure line is flatter). As a practical hint for exams, you should not assume a change in the MPC unless we describe such a change explicitly. b. True. The tool we use to analyze the determination of normal investment and the normal real interest rate is the saving and investment diagram. Investment demand is determined by firms decisions about how much new capital to buy, and is a decreasing function of the real interest rate. That is, I is a decreasing function of r*. The supply of saving, S, equals, Y* G* C*. Since a rise in r* increases the opportunity cost of current consumption in terms of future consumption, current consumption is an increasing function of r* which means that S is an increasing function of the r*. In the diagram, and are the initial investment demand and saving supply curves. r* r 1 r 2 S 2 S*,I* The place where normal or potential output enters the saving and investment diagram is the supply of saving curve. An increase in potential output affects Y* G* C* at a given real interest rate in two ways. First, and most obviously, this corresponds to an increase in Y*. Second, since income affects consumption, C* at a given real interest rate rises as well. However, the two effects are not equal and opposite: because households spend part of an increase in disposable income but also save some of it, C* at a given real interest rate rises by less than the amount of the increase in Y*. Thus, the supply of saving curve shifts to the right (from to S 2). The normal real interest rate, r*, falls (from r 1 to r 2 ), and normal investment, I*, rises (from to ).