# Profit Maximisation, Full cost, Pricing And Sales Maximisation

__Introduction__

The prime aim of the neo-classical theory of the firm has been profit optimisation. But empirical proof overwhelming point towards other objectives of firms, such as sales optimisation, output optimisation, contentment optimisation and utility optimisation etc.

__Profit Maximisation Theory__

The firm maximises its profits when it satisfies the two rules. MC = MR and the MC curve cuts the MR curve from below. Maximum profits refer to pure profits which are excess above the average cost of production. It is the amount left with the entrepreneur after he has made payments to all factors of production, including wages of management. In other words, it is a residual income over and above his normal profits. The profit maximisation condition of the firm can be expressed as:

Maximise p (Q)

Where p (Q) = R(Q) – C(Q)

While p (Q) is profit, R(Q) is revenue and C(Q) are costs and Q are the units of output sold. The two marginal rules and the profit maximisation condition stated above are applicable both to a perfectly competitive firm and to a monopoly firm.

Profit Maximisation theory is based on the following Postulations.

__Postulations__

- The objective of the firm is to maximise its profits where profits are the difference between the firm’s revenue and costs
- The entrepreneur is the single owner of the firm
- Tastes and habits of consumers are given and are invariable
- The firm produces a single, perfectly divisible and standardised commodity
- The firm has complete knowledge about the amount of output which can be sold at each price
- The firm’s own demand and costs are known with certainty
- New firms can enter the industry only in the long run. Entry of firms in the short run is not possible
- The firm maximises its profits over some time horizon
- Techniques of production are given
- Profits are maximised both in short run and long run

Based on the above postulations, the profit maximising model of the firm can be shown under perfect competition and monopoly.

__Profit Maximisation under Perfect Competition__

Under Perfect Competition the firm is one among large number of producers. It cannot influence the market price of the product. It is the price taker and quantity adjuster. It can only decide about the output to be sold at the market price. Hence, under conditions, of perfect competition, the MR curve of a firm coincides with its AR curve. The MR curve is horizontal to the X axis because the price is set by the market and the firm sells its output at that price. The firm is thus, in equilibrium, when MC = MR = AR (Price). The equilibrium of the profit maximisation firm under perfect competition and is represented in the diagram 1, where the MC curve cuts the MR curve first at point A.

It satisfies the condition of MC = MR, but it is not a point of maximum profits because after point A, the MC curve is below MR curve. It does not pay the firm to produce the minimum output when it can earn larger profits by producing beyond OM. It will however, stop further production the minimum output when it reaches the OM1 level of output where the firm satisfies both conditions of equilibrium. If it has any plans to produce more equilibrium point B. Thus the firm maximises its profits at M1B price and at output level OM1.

__Profit Maximisation under Monopoly__

There being one seller of the product under monopoly, the monopoly firm in the industry itself. Therefore, the demand curve for its product is downward sloping to the right, given the tastes and incomes of its customers. It is a price maker which can set the price to its maximum advantage. But it does not mean that the firm can set both price and output. It can do either of two things. If the firm selects its output level, its price is determined by the market demand for its product. Or if it sets the price for its product, its output is determined by what consumers will take at that price.

In any situation, the ultimate aim of the monopoly firm is to maximise its profits. The conditions for equilibrium of the monopoly firm are (1) MC = MR < AR (Price) and (2) the MC curve cuts the MR curve from below. It is represented in the diagram 2, that the profit maximising level of output is OQ higher than MR, and the level of profit will fall. If cost and demand conditions remain the same, the firm has no incentive to change its price and output. The firm is said to be in equilibrium.

An illustration will let us know the optimisation of profits, revenue, sales and output.

__Illustration__

An industry faces demand curve given by 2Q = 200 – 4P. Marginal and Average Costs for the industry are invariable at $20 per unit. Ascertain the following:

- What must be the level of productivity, should the industry manufacture to optimise profits,
- To Optimise Sales Revenue,
- Ascertain the corresponding profits at each productivity level.

__Solution____Condition
1__

The demand function is specified, that is 2Q = 200- 4P.

We have to first convert the demand function into inverse function. Thus we derive the following.

4P = 200 – 2Q

P = __200 – 2Q__

4

P = 50 – __Q__

2

Now, after obtaining this value, we have to equate MR with MC, for which we need to derive Total Revenue TR.

Total Revenue = Price x Quantity, Hence,

P **.** Q = 50Q – __Q^2__

2

Now, to obtain the Marginal Revenue, we have to apply the formula, __dP.Q__

**dQ**

This gives, 50 – Q

MC = AC = $20

Equating, MR with MC, to find out profit maximising output level, we have, 50 – Q = 20.

Now we can ascertain Q, with which we can determine the Price P.

Q = 50 – 20 = 30.

Substituting Q in the derivative P = 50 – Q / 2, we get the value of P to be,

P = 50 – (30) / 2

= 50 – 15 = 35.

**Hence Q = 30, P = 35**

__Condition (ii)__

Maximisation of Sales Revenue:

Sales Revenue is maximised at the output level, whose revenue TR is maximum. TR is maximum at the output level at which MR = 0.

Thus setting MR function obtained above as zero, we get

50 – Q = 0

**Hence, Q = 50.**

__Condition (iii)__

Profits at Profit optimising output level 30 are:

Profits = TR – TC

- ⇒ P.Q – AC.Q
- ⇒ (35 x 30) – 20(30)
- ⇒ 1050 – 600
- ⇒
**$800**

To obtain profits at sales revenue optimising level 50 we substitute Q = 50 in the inverse demand function, we obtain is:

Profits = (50 – Q^2 / 2) – (AC x Q)

- ⇒ [50 x 50 – (2500/2)] – (20 x 50)
- ⇒ 2500 – 1250 – 1000
- ⇒
**250**

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**Other topics under Product Pricing:**

- Applications of Demand and Supply Analysis under Perfect Competition
- Concepts of Revenue
- Derived Demand, Joint Supply
- Determination of Profit Maximisation under monopolist situation
- Duopoly and Oligopoly
- Equilibrium of the Firm and Industry
- Forms of Market Structure
- Importance of Time Element in Price Theory
- Joint Demand Supply
- Linear Programming
- Long Run Equilibrium of Firm and Industry
- Market Structures
- Monopolistic Competition
- Monopsony and Bilateral Monopoly, Price output Determination
- Objectives of Business Firm
- Oligopoly, Cournot's Oligopoly Model
- Pricing of Public Undertakings
- Pricing Under Perfect Competition - Demand Supply - Basic Framework
- Profit Price Policy
- Resource allocation under monopoly
- Short, Long Run Supply Curve of the Firm and Industry
- Similarities and Dissimilarities between Monopoly Competition and Perfect Competition
- Supply Its Law - Elasticity and Curve
- The Nature of Costs and Cost Curves
- Williamson's Utility Maximisation