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Help 1118799062.reader.chegg.com Pandora Radio-Listen to Free omework for Chapter 6- Intermediate... Microeconomics What can you say about the returns to scale of the production function Q = aK+bL, where a and b ositive constants? c) What is the elasticity of substitution for this produc- tion function? 6.24. ConsideraCES production function gven by Q = What canyou say abouheWhaasticity of substution for this produc- tief production function Q = min(aK, bL), where a are positive constants? tion function? b) Does this producton function exhbit increasing, de- . A firm produces a quantity Q of breakfast cereal creasing, or constant returns to scale? g labor L and material M with the production func- c Suppose that the production function took the form n 0-50VML + M + L" The marginal product Q = (100 + Kos + LOS. Does this producton funaon ctions for this production function are exhibit increasing, decreasing,or constant returns to scale? 6.25. Consider the following production functions and their asociated marginal producs. For each produc- tion function indicate whether (a) the marginal prod- uct of each input is diminishing, constant, or increasing in the quantity of that input; (b) the production func- tion exhibits decreasing, constant, or increasing returns MPL = 25 +1 a) Ar the reurns to scde inceasing, consant, or de- to scale. creasing for this production function? Marginal Marginal Product of Product ofReturns to Function Labor? Capital? MPx Scale? MPL-1 MPK-1 1 VL VL 2 VK MP-K MPc L

Explanation / Answer

Returns to scale – refers to how much additional output can be obtained when we change all inputs proportionately.

Solving the above equations to find whether we have Decreasing Constant or Increasing returns to scale:

1.Q=L+K

Y0=F(K,L) = K+ L (Initital Equation)

Y1=F(zK,zL) = zK+ zL (Pulling out z from the equation) (Final Equation)

=z(K+L) =Y0

Thus z*Y0=Z*Y0 = Constant returns to scale

2.Q=sqrt(KL)

Y0=F(K,L) = sqrt(KL)

Y1=F(zK,zL) = zK^0.5*zL^0.5 (Pulling out z from the equation) (Final Equation)

=z^0.5*z^0.5*(K^0.5*L^0.5 )=Y0

=z^1*Y0 =z*Y0) =Constant returns to scale

5.Q=L^3K^3

Y0=F(K,L) =L^3K^3

Y1=F(zK,zL) = zL^3zK^3 (Pulling out z from the equation) (Final Equation)

z^3*z^3*L^3K^3

z^6*Y0>z*Y0 =Increasing returns to scale

4.Q=L*K

Y0=F(K,L) = L*K

Y1=F(zK,zL) = zL*zK

z^1*z^1*Y0

=z^2*Y0>z*Y0= Increasing returns to scale

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