Question

A firm production function is given by q(l,k) = l0.5·k0.5, where q is number of units of output produced, l the number of units of labor input used and k the number of units of capital input used. In the short-run the firm’s amount of capital is fixed at k1 = 100. When l = 25, the firm’s marginal product of labor is [MPl].

Answer 1

Answer

the MPl is found by differentiation of the given production function

q(l,k)=l^(0.5)k^(0.5)

k=100 then

q=l^0.5 *100^(0.5)=10l^0.5

dq/dp=5/l^0.5

l=25 then

MPl=5/l^0.5=5/(25^0.5)=1

the MPL is 1 units

q(l,k)=l^{0.5}k^{0.5}\\
k=100\\
q(l,k)=l^{0.5}*100^{0.5}=10l^{0.5}\\
MPL=\frac{\partial q}{\partial l}=\frac{\partial 10l^{0.5}}{\partial l}=\frac{5}{l^{0.5}}\\
l=25\\
MPL=\frac{5}{25^{0.5}}=1\\