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The profits of a competitive firm

September 27, 2011 Comments off

In the long run when a market is perfectly competitive, all firms will make zero profit, but in the short run firms can make profits (this is what attracts new firms into the market and increases the market supply).

As the firm cannot influence the price by setting its level of output, it just receives a price P on every unit it sells. So its total revenue will be $TR=PQ$ and its marginal revenue will be $MR = \frac{d(TR)}{dQ} = P$.

So in a competitive market price equals marginal revenue.

To maximise its profit, a firm sells where its marginal revenue equals its marginal cost, so in a competitive market, a firm sells where price equals marginal cost.

Let’s consider a firm in a competitive market which faces an inverse demand function of $P=20$

The firm has fixed costs of $FC=2000$ and variable costs of $VC=0.4q^{1.5}$

So its total cost is $TC = FC + VC = 2000 + 0.4q^{1.5}$.

Its marginal cost is $MC = \frac{d(TC)}{dq} = 0.6q^{0.5}$.

It sets its production level where P=MC, so

$20 = 0.6q^{0.5} \Rightarrow 33.333 = q^{0.5} \Rightarrow q = 1111.111$

What profits does it earn at this point?

Profit is equal to total revenue minus total cost, so

$\pi = TR - TC = Pq - FC - VC = 20(1111.111) - 2000 - 0.4(1111.111)^{1.5} = 5407.407$

Notice that the marginal cost is not affected by the amount of the fixed cost. If the firm had say, fixed costs of 4000, then it would still produce an output of 1111.111, it would just find that its overall profits were down to 3407.407.

The level of fixed cost affects the overall profits, but it does not affect the overall profit maximising amount.

The price taking firm

August 13, 2011 Comments off

In a perfectly competitive market, the firm is a price-taker, it cannot influence the market price through the quantity it produces. In practice this means the firm is so small in proportion to the overall market that it has no market power, so it can sell any quantity it is able to produce at the market price.

The overall market price is determined by the market supply (provided by all the firms in the market) and the market demand (demanded by all the consumers in the market). The firm can sell any quantity it can produce at the market price, so even though the market is likely to face a downward sloping market demand curve, the individual firm faces a horizontal market demand curve at the market price. Because the firm can sell as much as it can produce at the market price, the marginal revenue for each unit sold is equal to the price, and the average revenue is also equal to the price, as every unit costs the same, so when you divide the total revenue by the number of units sold, you get the price.

The price-taking firm will observe two rules:

Marginal output rule – the firm will produce at an output where the price is equal to the marginal cost of production (MR = MC, and here P = MR so P = MC)

Shutdown rule – the firm will shut down if the average revenue is lower than the average cost at all output levels, so as the price equals average revenue, it will shut down if the price is lower than the average total cost at all levels.

We can look at this in terms of graphs:

This is the market supply and market demand. The equilibrium market price is P1.

This is the firm’s supply and demand graph. The firm’s supply curve is the marginal cost of production, and it faces a horizontal demand curve at the market price of P1. So it produces quantity q1, the point where price equals marginal cost. Here the firm is able to make some profit $\pi$ because at point q1 the average revenue (the price) is greater than the average total cost. This is a short run situation, because when other people see that there are profits to be made in the industry, it will attract the entry of new firms to the market.

The arrival of the new firms expands the market supply to S2, which drives down the equilibrium market price to P2.

At P2, the price has been driven to the level where the firm produces at point q2, where the price is equal to the marginal cost and the average total cost. At this point because the average revenue (price) is equal to the average cost, there is zero profit. So now you reach an equilibrium point. No new firms will enter the industry as there are no profits to be made, firms are just breaking even. But no firms will leave the industry as they are not making losses and are not in the shutdown position. Remember that perfect competition assumes that the firms are identical and face identical cost functions.

So firms in a perfectly competitive market can make profits in the short run, but will make zero profit in the long run.

What makes a market competitive?

The idea of perfect competition is like the Holy Grail in economics, many economic models start from the premise of perfect competition as a fundamental assumption, which is pretty unrealistic. But it is really important to understand perfect competition because it is the centrepiece of anything to do with markets in microeconomics.

A perfectly competitive market will have these four characteristics:

Sellers are price takers – each seller is sufficiently small in relation to the overall market that they can’t influence the market price by their own production decisions. Because of this no firm believes that it can influence the behaviour of other firms. This isn’t the case with other forms of market structure where there is some element of market power…and a firm with a large market share can influence the market price by varying the level of output it chooses to produce.

Buyers are price takers – each buyer is sufficiently small in relation to the overall market that they can’t influence the market price by the amount they consume.

Sellers do not engage in strategic behaviour – when a firm makes its own output decisions, it does not take into consideration the response of other firms (as it doesn’t expect them to change their behaviour as a result of their decisions).

Firms can enter and exit the market freely – there are no barriers to entry such as prohibitive start up costs or difficulties obtaining licences to produce.

In order for these four characteristics to be present, you will usually need to have:

A large number of sellers and buyers – so that the first two assumptions hold, no individual can influence the market price.

Highly substitutable goods – if one seller reduced the price, consumers would switch away from the other firms, because the good in question is easily substitutable from one firm to another. This will not happen if the firms can differentiate between their brands, ie a firm with market power may be able to get away with charging a higher price than a rival and still get sales, because consumers prefer that brand. But if they are producing something which is basically identical (eg ball bearings of standard size) then people will just buy from the firm that sells it cheapest. This characteristic pushes price down to the lowest possible level that firms can still cover their costs to produce the good.

Buyers must have full information – if a firm were to raise its price, consumers would know that rival firms sell it cheaper and could switch away to them. They have to have full information available about the alternatives.