Question: A paint manufacturing company has a production function Q = K + L. For this production function MPK = 1 and MPL = 1/(2L). The

A paint manufacturing company has a production function Q = K + √L. For this production function MPK = 1 and MPL = 1/(2√L). 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?
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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