Practical Management Science
Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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7.17. A paint manufacturing company has a production function Q = K+ VLQ = K + vVL. For this production function MPK=1 and MPL = 1/ (2/L) MPL = 1/(2 VL). The firm faces a price of labor w that equals $1 per unit and a price of
capital services r that equals $50 per unit.
a) Verify that the firm's cost-minimizing input combination to produce Q= 10 involves no use of capital.
b) What must the price of capital fall to in order for the firm to use a positive amount of capital, keeping Q at 10 and w at 1?
%3D
c) What must Q increase to for the firm to use a positive amount of capital, keeping w at 1 and r at 50?
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Transcribed Image Text:7.17. A paint manufacturing company has a production function Q = K+ VLQ = K + vVL. For this production function MPK=1 and MPL = 1/ (2/L) MPL = 1/(2 VL). The firm faces a price of labor w that equals $1 per unit and a price of capital services r that equals $50 per unit. a) Verify that the firm's cost-minimizing input combination to produce Q= 10 involves no use of capital. b) What must the price of capital fall to in order for the firm to use a positive amount of capital, keeping Q at 10 and w at 1? %3D c) What must Q increase to for the firm to use a positive amount of capital, keeping w at 1 and r at 50?
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