Suppose a firm’s long-run production function is given by Q=K^0.25 L^0.25 ,where K is measured in machine-hours per year and L is measured in hours of labor per year. The cost of capital (rental rate denoted by r) is $1200 per machine-hour and the cost of labor (wage rate denoted by w) is $12 per hour.
Hint: if you don’t calculate the exponential terms (or keep all the decimals when you do), you will end up with nice numbers on all parts below.
Short run production function is given by
Marginal Product of labor is given by
We can see that as L increases, Q increases.
As L increases, MPL decreases.
So, we can say that MPL is decreasing for all increasing level of output.
MPL is decreasing for Q>0
We have derived in part i that
L=Q4/12000=6004/12000=10,800,000 labor hours
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