Algebraic expressions of the production function
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#2) Following are different algebraic expressions of the production function. Decide whether each one has constant, increasing, or decreasing returns to scale.
a. Q = 75L0.25 K0.75
b. Q = 75A0.15 B0.40 C0.45
c. Q = 75L0.60 K0.70
d. Q = 100+50L+50K
e. Q = 50L+50K+50LK
f. Q = 50L2 + 50K2
g. Based on the answers for the preceding equations, can you make any generalizations about the functional form of a production equation, the relative magnitudes of the coefficients, and the nature of the returns to scale? Explain.
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The expert examines algebraic expressions for the production functions.
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To determine returns to scale, we need to know how much output increases for the same amount of input. If the greater amount of input yields less output, you have decreasing returns to scale. We can use a multiplier, m, to transform each equation and see how much output has increased.
a. Q = 75L^0.25 K^0.75
Q' = 75(L*m)^0.25(K*m)^0.75
We factor out m, add the exponents, and note that m^1 = m
= (75L^0.25 K^0.75) m
Now we substitute Q for the ...
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