In: Economics
Davy Metal Company produces brass fittings. Davy's engineers estimate the production function represented below as relevant for their long-run capital-labor decisions.
Q=500L0.6K0.8
where Q = annual output measured in pounds,
L = labor measured in person-hours,
K = capital measured in machine hours.
The marginal products of labor and capital are:
MPL=300L-0.4K0.8 , MPK=400L0.6K-0.2
Davy's employees are relatively highly skilled and earn $15 per hour. The firm estimates a rental charge of $50 per hour on capital. Davy forecasts annual costs of $500,000 per year, measured in real dollars.
The production function would be as
.
(a) The isocost equation would be as
or
.
(b) The isocost lines for the stated costs
would have the equation
or
. The graph would be as below.
(c) The optimal capital labor ratio would be
where
or
or
or
or
.
(d) For the isocost be
and the optimal capital labor ratio as
or
, we have
or
or
, and since
, we have
or
or
.
These are the required optimal input combination for the given budget.
(e) The output would be as
or
or
units.
(f) (1) The capital labor ratio would be as
where
or
or
or
or
or
. As can be seen, the optimal capital per labor required
increased.
(f) (2) Putting this in the isocost line, we
have
or
or
or
and
or
or
. The output in this case would be
or
or
units.
As can be seen, the output has decreased due to increase in the wages.