Unformatted text preview: hich is assumed to be strictly positive)
which is, of course, impossible.
Case B
When is
⏟?
When is 4
ECO 204 Chapter 14: The Mathematics of the Profit Maximization Problem (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. This says the company should produce at capacity (which is assumed to be strictly positive). Therefore we know that
To see when Case B arises we need to see when
. Substitute
and
in the FOC: ⏟ ⏟ ⏟ Now: This says that if the marginal revenue at capacity is greater than or equal to the marginal cost at capacity then the firm
should produce at 100% capacity which will happen when capacity is less than or equal to the unconstrained solution
(why?). In case B
, which allows us to reinterpret the FOC. From the envelope theorem recall that
so that the FOC for case B can be written as: ⏟ ⏟ ⏟ ⏟ ⏟ ⏟ Intuitively, the firm will produce at full capacity when the capacity is less than or equal to the “unconstrained optimal
output” (see example below). If the firm is producing at full capacity then at the optimal solution “marginal revenue =
total marginal cost” where the total marginal cost consists of the marginal cost of inputs used to produce an additional
unit of output plus the opportunity cost of allocating funds to produce output instead of expanding capacity. is a positive opportunity cost when capacity is less than the unconstrained solution (because in that case if resources that
have been used to produce output had instead been used to expand capacity, then it would’ve resulted in higher profits)
– see the graph below: 5
ECO 204 Chapter 14: The Mathematics of the Profit Maximization Problem (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Unconstrained solution Demand is a zero opportunity cost when capacity is equal to the unconstrained solution (because in that case if resources
that have been used to produce output had instead been used to expand capacity, then it would’ve resul...
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 Fall '14
 Economics, profit maximization problem, Sayed Ajaz Hussain

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