There are 2 main approaches on profit maximization problem:
- Total revenue to total cost
- Marginal revenue to marginal cost
- Total revenue to total cost.
According to this approach total profit (TP) is equal to total revenue (TR) minus total cost (TC).
TP = TR – TC.
TR and TC are functions of quantity (Q).
TR = f (Q) and TC = f (q).
In this case we look for a value of Q which outputs maximal value of P.
- Marginal revenue to marginal cost
It is an alternative perspective that relies on marginal profit value (MP) which is equal to marginal revenue (MR) minus marginal cost (MC).
MP = MR – MC
If MR is greater than MC at some value of quantity MP is greater than 0. This means that we will receive profit from the next produced item so we need to produce a greater quantity. On the opposite, if MP is less than zero it means that the next produced item will cause a loss, so we do not produce more (Lipsey, R. G., & Steiner, P. O. 1975).
According to this approach MP max will occur when marginal revenue is equal to marginal cost.
So if marginal revenue is greater than marginal cost (MR > MC) we produce a greater quantity until MR = MC.
If marginal cost is greater than marginal revenue (MR < MC) we decrease output until MR = MC.
Where t – number of period.
According to calculations provided in the table 1 MR has negative slope and decreases all the time.
MC=dTCdQ= TCt-TCt-1Qt-Qt-1
Where t – number of period.
According to calculations provided in the table 1 MC has positive slope and increases all the time.
Calculations provided in the table 1.
Using calculations in the table one we can determine quantity that maximizes company’s profit using both “Total revenue to total cost” and “Marginal revenue to marginal cost” approaches.
According to “Total revenue to total cost” optimal Q is 8 because TP reaches its max level of 540.
According to “Marginal revenue to marginal cost” optimal Q is 8 because at this point MC = MR = 80.
As we can see both methods give the same answer.
References
Lipsey, R. G., & Steiner, P. O. (1975). Economics (4th ed.). New York: Harper & Row.
