Question

1. (12 points) Consider the production function Q = KL2-L", and answer the following questions. a. (4 pts) Does this production function exhibit diminishing marginal product of capital? Diminishing marginal product of labor? Explain.

b. Does this production function have an uneconomic region? If yes, find the region.

c. Based on your answer to (b), sketch a graph of two isoquants Q1 and Q2 withQ1 < Q2.

Answer 1

Q=kL²-LS MPK = 0o = 2². ok м? - дв? .о. г. по MPK и mg оut thели it is not diminishing dka (112 MPL do = 2KL-SLY. a les at o m IMPL) = 0Q2 = 2K - 201² - OL 22² kkйло Коефи0 , os LicWoлo4 , д 4* xo 01 in the marquial product of labour is diminishing

function exhibits - the pred production diminishing MPL . b) Isoquants - they are combinations of inputs K& L the same output. &= [-LS Rewriting this, 18ths =k T22 you can table different values of K&L for a particular & & get me iso quant. MPLOI unesonomia Economic (feasible region is where marginal product of an input is positiu. Uneconomic region is where marginal product of an input is oor negative suice no producer will produce where marginal products are one of

24 iso quant is backward bending or upward sloping , men marginal product of any input will be negative & hence this portion is uneconomic Production is such region is unprofitable . the isoquant here has an upward sloping segment I marked in green) after a particular land of labour, heuce his region is me uneconomic region. At pourt o MPL is o nerefore, as we increase Cabour after his pourt , me MPL becomes -ue & hence it is not a feasible region ] . c) Lit 81=50 82=100 . using k= Qt is we form combinations of L&K fores L.2 each 819 82. Q1=50 eg til 2 3 4 & so on. k: 50 20.5 32.5 671125 suni larly for bom Q & Q2 we get different combinations Sy: 80 Стари o not scale ) $2=100 23s