4. 1) 2) 3) A bakeshop has the following production function for cupcakes: = 4K 0.5L0.5, (MPK = 2L0.5/K0.5, MP₁ = 2K 0.5/L0.5), where K is the quantity of capital, L is the quantity of worker hired. The cost of capital is r = $1000, and the cost of labor is w = $40 per worker. Does the production function exhibit diminishing marginal return of labor? Explain. Find the cost function of the bakeshop, C(Q). (Hint: Use the conditions MRTS = MP/MPK = w/r and Q = 4K 0.5 0.5, solve the optimal input choices K(Q) and L(Q). Then the cost function is given by C(Q) = r K(Q) + w L(Q)). Does the bakeshop experience economies of scale, diseconomies of scale, or neither? Explain with the calculation of scale economies index.
4. 1) 2) 3) A bakeshop has the following production function for cupcakes: = 4K 0.5L0.5, (MPK = 2L0.5/K0.5, MP₁ = 2K 0.5/L0.5), where K is the quantity of capital, L is the quantity of worker hired. The cost of capital is r = $1000, and the cost of labor is w = $40 per worker. Does the production function exhibit diminishing marginal return of labor? Explain. Find the cost function of the bakeshop, C(Q). (Hint: Use the conditions MRTS = MP/MPK = w/r and Q = 4K 0.5 0.5, solve the optimal input choices K(Q) and L(Q). Then the cost function is given by C(Q) = r K(Q) + w L(Q)). Does the bakeshop experience economies of scale, diseconomies of scale, or neither? Explain with the calculation of scale economies index.
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.1P
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Transcribed Image Text:4.
A bakeshop has the following production function for cupcakes:
1)
2)
3)
Q
= 4K 0.5 L0.5, (MPK = 2L0.5/K0.5, MP₁ = 2K 0.5/L0.5),
where K is the quantity of capital, L is the quantity of worker hired. The cost of
capital is r = $1000, and the cost of labor is w = $40 per worker.
Does the production function exhibit diminishing marginal return of
labor? Explain.
Find the cost function of the bakeshop, C(Q). (Hint: Use the conditions
MRTS =MPL/MPK = w/r and Q = 4K 0.5 L0.5, solve the optimal input choices
K(Q) and L(Q). Then the cost function is given by C(Q) = r K(Q) + w L(Q)).
Does the bakeshop experience economies of scale, diseconomies of
scale, or neither? Explain with the calculation of scale economies index.
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