Question

Let a production function for a country, Eastasia, be defined
as: Y=5*L^{1/3}*K^{2/3}.

Suppose L=27 and K=64. Find the level of GDP.Now, suppose L=13.5 and K=32. Find the level of output in the economy.

Does this function have constant returns to scale? Explain.

Now, let
Y=5*L^{1/3}*K^{2/3}+L. Does this function have
constant, increasing, or decreasing returns to scale? Explain.

Answer #1

1) Level of GDP when L = 27 and K = 64

GDP = 5 x 27^{1/3} x 64^{2/3} = 240

when L = 13.5 and K = 32

Output = 5 x 13.5^{1/3} x 32^{2/3} = 120

The function has constant returns to scale because when the inputs are halved, the output is also halved. (can be seen in the example above)

Y = 5 x L^{1/3} x K^{2/3} + L

When L and K are both doubled:

Y' = 5 x (2L)^{1/3} x (2K)^{2/3} + 2L

Y' = 10 x L^{1/3} x K^{2/3} + 2L = 2Y

The function has constant returns to scale because when the inputs are doubled, the output is also doubled.

Suppose a competitive firm’s production function is Y= 20
L1/2 K1/3. L is Labor , K is capital and Y is
output.
a) (4) Find the marginal product of labor and capital.
b) (4) What is Marginal Rate of technical Substitution of Labor
for Capital?
c) (2) Does this production function exhibit increasing,
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Consider the following production function: Y = A ̄K2 L1 , where
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A firm produces output according to the production function.
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(d) Find the firm's long-run total cost function...

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max Y = 100K0.25N0.75
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