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2) Given the Cobb-Douglas production function for Mabel’s factory Q = (L0.4) * (K0.7) a) Based...

2) Given the Cobb-Douglas production function for Mabel’s factory Q = (L0.4) * (K0.7) a) Based on the function above, does Mabel’s factory experiencing economies or diseconomies of scale? Explain. b) If the manager wished to raise productivity by 50% and planned to increase capital by 25%, how much would she have to increase her labor to reach that desired production level?

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Answer #1

2) Q=L0.4K0.7  

since Above production function exhibits increasing returns to scale which means factory is experiencing economies of scale.

b) Log Q=0.4Ln L+0.7LnK

Totally Differentiating with respect to time

then

growth rate of output/production= 0.4 growth rate of labor+0.7 growth rate of capital

50=0.4(25)+0.7 growth rate of population

0.7(growth rate of population)=50-10=40

Growth rate of population=40/0.7=57.14285%

labor should increase by 57.14285%

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