191hw3sol

191hw3sol - ECON191 Spring 2009 Outline of suggested...

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1 ECON191 Spring 2009 Outline of suggested solutions to Problem Set 3 (1) Given, MPL = 3(K/L) 0.25 , MPK = (L/K) 0.75, P L = $3/unit, P K = $1/unit, P K K + P L L = 8 Cost is minimized when MPL/P L = MPK/P K (K/L) 0.25 = (L/K) 0.75 L = K Total cost of production P K K + P L L = 8 3L + K =8 K = L = 2 units The level of production: Y = 4K 0.25 L 0.75 Y= 4(2) 0.25 (2) 0.75 = 4(2 0.25+0.75 ) = 8 units (2) (a) MPL L + MPK K = 3(K/L) 0.25 (L) + (L/K) 0.75 (K) = 3K 0.25 L 0.75 + L 0.75 K 0.25 = 4K 0.25 L 0.75 =Y (b) (MPL L)/Y = 3K 0.25 L 0.75 / 4K 0.25 L 0.75 =0.75 (c) (MPK K)/Y = L 0.75 K 0.25 / 4K 0.25 L 0.75 = 0.25 (d) MPL is equal to real wage rate in the competitive market. MPL L is the total wages paid to the workers. Similarly, MPK K is total payment to providers of capital. The first equation tells us that output Y is exactly exhausted by payment to workers and capitalists. (This is true only of we have constant returns to scale, as is the case here.)
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191hw3sol - ECON191 Spring 2009 Outline of suggested...

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