Another firm in the same industry, Cake, considers setting up a plant in Canada and is thus evaluating its long-run production possibilities there. Besides using machinery K, it can hire labor L.
The production function is q = f(K, L) = K0.5L 0.5 .
Question:
a) What is the equation of the isoquant, i.e. K as a function of labor (and output)?
b) If you reduced labour input by one (small) unit, how many additional units of capital would you need to hold output constant?
c) The manufacturer estimates that it will sell 12 units of its product. How many additional units of capital do you need to substitute for one (small) unit of labor when L = 6? How many do you need when you want to substitute for one (small) unit of labor when L = 12? In which case do you need more additional capital?