Econ 302 Assignment 2 Answer Key

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1 Econ 302 Assignment 2 Answer ey Chapter (a) In the example in the text, region A uses technology f A (l) to produce output, while region B uses technology (with a higher MPL schedule), f B (l). If there were separate labor markets in the two regions, they would have separate wage rates given by MPL A (l A ) and MPL B (l B ) where l A and l B are household labor supply in regions A and B. When trade in labor opens up, which will equate real wages across regions, real wages paid by firms in region B will fall and in region A they will rise, because workers from region A will cross to region B to perform work. So you might think of the answer to this question being: workers from region A will like the single market, while workers from region B will not. It turns out that the reverse is true for firms. Because real wages rise in region A firms there also reduce labor input, and both effects tend to reduce profits. The reverse is true in region B, where falling real wages and rising labor input will raise profits. Hence, shareholders in region A are unhappy while shareholders in region B are happy. (b) In the real world, where ownership of firms is not allocated equally across the population, the effects of the opening of a single labor market could have an important political impact: if workers are not also shareholders, then workers in region B will be opposed to opening the single market, whereas firms in region B will be opposed. The opposite should be true in region A. 6.9 (a) In Chapter 5 we saw that a temporary parallel downward shift in the production technology lowers wealth, by a small amount, and therefore shifts C d slightly to the left. We also saw that it shifts Y s substantially to the left (see Figure 5.4). This lowers C and Y and raises R, the equilibrium interest rate. In the labor market diagram, we know that the increase in the interest rate shifts the labor supply curve to the right, and that labor demand is unaffected by the shock. So w/p should fall and L should increase. See Figure 1(a) (b) No. (c) The answer to (a) changes. A downward shift in MPL combined with the downward shift in f(l), i.e. a proportional shift of f(l), will have similar implications for C, Y and R. However, in the labor market diagram, at the same time as the labor supply curve is shifting to the right, the labor demand curve will shift to the left. Then there will be excessive labor supply at the original (w/p)*. Real wage has to decrease to (w/p)*' to clear the market. But the

2 equilibrium L is ambiguous. We usually assume the effect on labor demand is strong enough to outweigh the effect on labor supply so that both w/p and L should fall. See Figure 1(b).

3 Chapter (a) According to one way of thinking about this question is that the price of consumables equals the price of capital because there is no real distinction between the investment good and the consumption good. If someone wants a consumption widget or an investment widget they just go to the single widget market and purchase the widget for whatever purpose they want to use it for. If the prices were different then nobody would buy the more expensive widgets. Another way to think about it is that they are distinct goods but the technology for producing them is identical and they use the same inputs. Then they have to have the same price because otherwise producers would only produce the more expensive one. (b) If for some reason investment demand was so low that aggregate I d was actually negative, then the price for investment goods would fall below the price of consumption goods, and production of investment goods would be zero. (c) No, the prices could be different because the marginal rate of transformation between consumption and investment goods would no longer be Method 1: Think about the return to investment. If I buy a unit of investment at time t, the government will give me back a fraction a of its cost, so my net purchase cost will be (1 a)pt. The payoff at t+1 will be Pt+1MPt+Pt+1(1 a)(1 δ) because Barro assumes you have to give back the same percentage tax credit to the government if you resell the capital. Hence, the nominal return to capital is Pt+ 1MPt+ P t+ 1(1 a)(1 δ ) (1 a)p which must equal 1 + Rt in equilibrium. Hence we get the result MPt = (rt + δ)(1 a) whereas if the tax credit was not in place we would have MPt = rt + δ Clearly the higher the tax credit, 0 a < 1, the lower MPt will be, and hence the higher desired capital and investment demand will be. (Refer to Figure 9.6, moving along the curve) Method 2: W The profit function is π = Y ( r+ δ) (1 α) L P Again, we have MPt = (rt + δ)(1 a) t

4 Chapter Use the formulas Lt+1 = (1 σ)lt + φut Ut+1 = σlt + (1 φ)ut with σ = 0.01 and φ = 0.2. In this case the natural unemployment rate is σ/(σ + φ) = 0.01/0.21 = , or just under 5 percent. We would expect to see about 4.76 million unemployed in the long-run in this economy since the labor force is 100 million. We can illustrate the paths of Lt and Ut using a table: time employment unemployment separation finding u. rate:

5 time paths of employment and unemployment millions time period separation finding

6 Fall 2012 ECON 302 Intermediate Macroeconomics Professor Ananth Seshadri Assignment 2 Answers Preliminary 11.8 Y = F (, L) exhibitscrs,soy/l = F (,L) = F (/L, 1) f(/l). This shows output L per capita is a function of capital per capita, and f has diminishing return (a) At the steady state, sa L 1 = ) =( sa ) 1 1 L. (b) I = = ( sa ) 1 1 L. C =(1 s)y. (c) (d) = sy = sa( L )1. From the above equation, because 0 < <1, so as increases, decreases. Y Y = = (sa( L )1 ). Y isinthedenominator,so decreases with, but it is independent from Y. Y (a) Since all economies have the same steady state values, absolute convergence holds here. To see poor economies grow faster than rich ones, take partial @ ( ( Y/ Y / ) Y 2 Y / < 0 because Y has constant return to scale. A CRS function F (, L) hasthefollowing property: F (, @L L. Y L<0 1

7 (b) If economies have di erent steady state value, the concept of absolute convergence can not hold anymore. However, conditional convergence holds. For more details, please read the Handout 6. (c) All the results in the Solow growth model, includes this convergence concept, are abased on the constant saving rate. If the saving rate varies over time, the rate of convergence would depend on how exactly s(t) changes (a) (b) (c) sf (, L) isnowastraightline. = sa =(sa ) = sa Y = ) Y Y = = sa So Y and grow at the same rate, and there is no steady state. property can not hold here. The convergence (d) If there is no diminishing return to capital, the steady state would not exist, like this problem This problem is the same as problem 11.13, which we discussed in the Handout 6, Ex4, the e ect of population growth. Now even L is a constant, but due to improvement of human capital, ˆL, whichisusedintheproductionfunction,theoutputandcapitalgrowat the rate x in the long run. (a) Now e ective labor ˆL grows at the rate x. Thisdoesnotchangethe, Eq(11.2)still holds. Since the steady state value,y increase as labor increases, these values are not constant. 2

8 (b) We know the steady state of (/ˆL) exists. 0= = sf (, ˆL) ˆL =sf (/ˆL, 1) = ˆL ˆL ˆL 2 = ˆL ˆL ˆL x x ˆL. ˆL ˆL ˆL (c) This technology progress in labor has the same e ect as population growth. Output per e ective labor will tend toward to a constant value (Y/ˆL). But since L is a constant, Y grows at the rate x, outputper capita Y/L grows at the rate x as well. This technology progress leads to a constant growth of per capita output. 3

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