Problem Set 2 FE312 Fall 2011 Rahman. Some Answers

Transcription

1 Poblem et 2 ome Anses 1) Use the neoclassical theoy of distibution to pedict the impact on the eal age and the eal ental pice of capital of each of the folloing events (illustate gaphically, using to gaphs fo each case, one fo the labo maket and one fo the capital maket, and explain in one o to sentences): a. A ave of immigation inceases the labo foce. Accoding to the neoclassical theoy of distibution, the eal age equals the maginal poduct of labo. Because of diminishing etuns to labo, an incease in the labo foce causes the maginal poduct of labo to fall. Hence, the eal age falls. Because capital is no REATIVEY moe scace, it becomes moe poductive hence demand fo capital by fims ises. Page 1 of 5

2 b. An eathquake destoys some of the capital stock. Poblem et 2 The eal ental pice equals the maginal poduct of capital. If an eathquake destoys some of the capital stock (yet miaculously does not kill anyone and loe the labo foce), the maginal poduct of capital ises and, hence, the eal ental pice ises.. Because labo is no REATIVEY moe abundant, it becomes less poductive hence demand fo labo by fims ises. c. A technological advance impoves the poduction function. If a technological advance impoves the poduction function, this is likely to incease the maginal poducts of both capital and labo. Hence, the eal age and the eal ental pice both incease though inceases in demand fo both factos. Page 2 of 5

3 Poblem et 2 2) uppose that the poduction function is Cobb-ouglas. That is, the poduction 1 function is Y F(, ) A. a) olve fo the faction of income paid to capital (sho you ok). Y MP A 1 1. Of couse, *MP is the total income paid to capital. Thus the FRACTION of income paid to capital is simply hich is simply. * MP Y, b) ay α = 0.3, and suppose that immigation aises the labo foce by 10 pecent. What happens to total output (in pecentage change)? The eal ental pice of capital (in pecentage change)? The eal age (in pecentage change)? Y 1 = A , Y 2 = A 0. 3( ) Y 2 / Y 1 = (1.1) 0.7 = (R/P) 1 = MP = 0.3A , (R/P) 2 = 0.3A -0.7 ( ) (R/P) 2 / (R/P) 1 = (W/P) 1 = MP = 0.7A , (W/P) 2 = 0.7A -0.7 ( ) (W/P) 2 / (W/P) 1 = Thus e see that hile output and the ental ate of capital each ise by 6.9%, the age falls by 2.8%. c) ay α = 0.3, and suppose that a gift of capital fom aboad aises the capital stock by 10 pecent. What happens to total output (in pecentage change)? The eal ental pice of capital (in pecentage change)? The eal age (in pecentage change)? Page 3 of 5

4 Y 1 = A , Y 2 = A( ) 0.7 Poblem et 2 Y 2 / Y 1 = (1.1) 0.3 = (R/P) 1 = MP = 0.3A , (R/P) 2 = 0.3A( ) 0.7 (R/P) 2 / (R/P) 1 = (W/P) 1 = MP = 0.7A , (W/P) 2 = 0.7A( ) -0.7 (W/P) 2 / (W/P) 1 = Thus output ises by 2.9%, ental ates fall by 6.5%, and ages ise by 2.9% d) ay α = 0.3, and suppose that a technological advance aises the value of the paamete A by 10%. What happens to total output (in pecentage change)? The eal ental pice of capital (in pecentage change)? The eal age (in pecentage change)? Eveything goes up by 10%. 3 a) uppose an automobile manufactue is choosing beteen to poduction options. It can poduce 100 cas ith 200 okes and 50 machines, o it can poduce 166 cas ith 300 okes and 75 machines. Would you descibe the manufactue s poduction function as exhibiting deceasing, constant, o inceasing etuns to scale? Explain. The capital stock and the labo foce incease by 50% and the output inceases by 66%. This is inceasing etuns to scale. b) Regadless of hat you anse as in pat a, e can say that this manufactue faces diminishing maginal poductivity fo both machines and okes. Explain ho this is possible. Inceasing etuns to scale efes to the change in output hen both factos ae inceased in the same pecentage. iminishing maginal poductivity descibes the change in output hen only one facto is alteed. Page 4 of 5

5 Poblem et 2 4) Conside to competitive economies that have the same quantities of labo ( = 400) and capital ( = 400), and the same technology (A = 100). The economies of the counties ae descibed by the folloing Cobb-ouglas poduction functions: Noth Economy: outh Economy: Y Y A A a) Which economy has the lage poduction? Explain. Output is the same in both economies, given the symmety of the paametes of the poduction functions and the equal quantities of labo and capital. b) In hich economy is the maginal poduct of labo lage? Explain. The MP is lage in the outh Economy. The MP depends on the value of (1-α) and the aveage poductivity of labo (Y/). ince the aveage poductivity of labo is the same in both counties, diffeences in the MP depend on the value of (1-α), hich is lage in the outh. c) In hich economy is the eal age lage? Explain. ince factos ae paid accoding to the values of thei maginal poducts, the eal age is lage in the outh Economy, because the MP is lage in the outh. d) In hich economy is labo s shae of income lage? Explain. abo s shae of incomes equal (1-α), hich is again lage in the outh. Page 5 of 5