Tharikha Arun Assignment 2 Professor Debasis Rooj 9th Septemper, 2016 1.The following data give real GDP, Y, capital, K, and labor, N, for the U.S. economy in various years. Year Y K N 1960 3109 3883 66 1970 4722 5863 79 1980 6450 8433 99 1990 8955 11,460 119 2000 12,560 15,402 137 2010 14,784 18,513 139 Units and sources are the same as in Table 3.1. Assume that the production function is Y=AK^0.3N^0.7. By what percentage did U.S. total factor productivity grow between 1960 and 1970? Between 1970 and 1980? Between 1980 and 1990? Between 1990 and 2000? Between 2000 and 2010? What happened to the marginal product of labor between 1960 and 2010? Calculate the marginal product numerically as the extra output gained by adding 1 million workers in each of the two years. (The data for employment, N, are measured in millions of workers, so an increase of 1 million workers is an increase of 1.0.) Ans 1. Year 1960 1970
Y 3109 4722
1980 1990
6450 8955
2000
12,560
K 3883 5863 8433 11,46 0 15,40 2 18,51 3
N 66 79 99 119 137
K^0.3 11.93302 13.50318 2010 14,784 139 15.05895 16.51032 18.04152 In order to check chane in MPN 19.66527 from 1960 to 2010, take N+1 to be the new N New Y 3141.90 4763.76
MPN 32.90 41.76
N^0.7 18.77936 21.29801 24.94277 28.37154 31.31154 31.63081 value:
A 13.87362 16.41916 17.17198 19.11733 22.23372 24.51538
% Change 18.3481 4.584999 11.32863 16.30136 10.26215
6495.54 9007.61 12624.11 14858.37
45.54 52.61 64.11 74.37
Therefore, MPN changed from 32.90 to 74.37 between 1960 and 2010. 5. Consider an economy in which the marginal product of labor MPN is MPN=3095−2N, where N is the amount of labor used. The amount of labor supplied, NS, is given by NS=22+12w+2T, where w is the real wage and T is a lump-sum tax levied on individuals. Use the concepts of income effect and substitution effect to explain why an increase in lump-sum taxes will increase the amount of labor supplied. Suppose that T=35. What are the equilibrium values of employment and the real wage? With T remaining equal to 35, the government passes minimum wage legislation that requires firms to pay a real wage greater than or equal to 7. What are the resulting values of employment and the real wage? Ans 5. MPN = 3095 – 2N = W (real wage) NS = 22+12w+2T NS = 22+12(3095 – 2N) +2T NS = 22 + 37140 – 24N + 2T At T = 35 NS = 22 + 37140 – 24N +2(35) NS = 37232 – 24N N = NS in the Equilibrium labour market 37232 = 25N N = 1489.28 W = 3095 – 2 (1489.28) W = 116.44 If a lump – sum tax is increased, there will be direct income effect and not a substitution effect. Increased tax will reduce labours wealth and so the labour supply increases.
If sales tax is increased in lump-sum, it will lead to a direct effect on the income and not on the substitution effect. Labour supply will then increase because of the increase in tax will lead to a reduction in wealth. Hence, The equilibrium employment is 1489.28 and wage is 116.44. At T = 35, and minimum real wage of 7 or greater W = 3095 – 2N 3088 = 2N N = 1544 NS = 22 + 12W + 2(35) NS = 92 + 12 (7) NS = 176 Therefore, at a real wage of 7, there is excess demand by 1368.
7. Consider an economy with 500 people in the labor force. At the beginning of every month, 5 people lose their jobs and remain unemployed for exactly one month; one month later, they find new jobs and become employed. In addition, on January 1 of each year, 20 people lose their jobs and remain unemployed for six months before finding new jobs. Finally, on July 1 of each year, 20 people lose their jobs and remain unemployed for six months before finding new jobs. What is the unemployment rate in this economy in a typical month? What fraction of unemployment spells lasts for one month? What fraction lasts for six months? What is the average duration of a completed spell of unemployment? On any particular date, what fraction of the unemployed are suffering a long spell (six months) of unemployment? Ans 7. Labour Force = 500 people Number of Unemployed people every month = 5 Nnumber of unemployed people every 6 months = 20 Therefore, 25 people are unemployed every month. Unemployment rate = Total number of spells during the year =(5 12)+ (20 2)
Threfore, 60 + 40 = 100; where, 60% of spells last for one month and 40% of spells last for 6 months. Average duration of completed spell of unemployment: (0.6 1 * one month)+ (0.46 * 6 months) = 3 months At any particular time, there are 25 people unemployed. 20 People unemployed for 6 months, suffer a longer spell. (20/25)100 = 80% 80% of unemployed suffer a longer spell Analytical Problems:
2.How would each of the following affect the current level of full-employment output? Explain. a)A large number of immigrants enter the country. b) Energy supplies become depleted. c)New teaching techniques improve the educational performance of high school seniors. d) A new law mandates the shutdown of some unsafe forms of capital. Ans 2. Full employment output is a term used to describe an economy that is operating with an ideal and efficient level of employment, where economic output is at its highest potential. When the economy is at full employment, aggregate demand is equal to aggregate supply. a) If a large number of immigrants were to enter a country, the number of people looking for employment will go up which means that the supply of labour will exceed the demand leading to a surplus of labour which in turn will lead to an increase in output as well. b) Because enrgy is a factor of production, a depletion in energy supplies will automatically lead to a reduction in current full-employment output. c) Although new teaching techniques will improve the educational performance of high-school seniors, they are still students in school and therefore have no contribution towards current level of output. Hence, the current level of fullemployment output remains unchanged. d) Capital is again a factor of production and with the shutdown of capital, there will be a direct decrease in the current full-employment output.
4. How would each of the following affect Helena Handbasket’s supply of labor? The value of Helena’s home triples in an unexpectedly hot real estate market. Originally an unskilled worker, Helena acquires skills that give her access to a higher-paying job. Assume that her preferences about leisure are not affected by the change in jobs. A temporary income tax surcharge raises the percentage of her income that she must pay in taxes, for the current year only. (Taxes are proportional to income in Helena’s country.) Ans 4. 1. If the value of Helena’s home tripples, it means that there is an increase in her wealth. This would result to an income effect where her desire to work would reduce thereby reducing her supply of labour. 2. If Helena acquired new skills that give her access to a higher paying job, then there is an increase in her real wage. Income effect comes into play and should reduces her supply due to her increase in real wage. However, she is not working longer hours to earn this increase in real wage, hence, her supply of labour does not change. 3. If the percentage of income that she has to pay as tax increases for the current year only, there would be only a temorary change in her real wage and hence will reduce her current labour supply temporarily.
