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Profit Maximization and Competitive Supply

Lecture PPTs A Damodaran

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Focus Perfect competition firm and industry Short run and long run supply curves

(or MC Curves) and equilibrium Effects of output Tax on supply

curves Producer Surplus vs Profits Constant cost, Increasing and

decreasing costs, supply curves for firm and industry

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Main Messages In PC a firm is a price taker: perfect elasticity

of Demand/Price/Average Revenue Curve MC=Supply Curve for a Competitive Firm MR=MC is profit maximization rule Also in Perfect Competition MC=Price = MR Producer surplus is R-VC is greater than

Profit which is R-VC-FC Shutdown of a firm when P< ATC for a firm

without sunk costs and P<AVC for a firm with sunk costs (thinks twice before closing???)

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Main Messages The industry supply curve can be increasing ,

decreasing or constant depending upon whether the inputs market is big or small to take in large number of firms that enter when prices of output are going up

A rise in input price will cause a firm to reduce its output as prices do not rise for a firm in a competitive market

So is the case of output tax

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Main Messages Though Zero profit is the norm for a

firm in a competitive industry sometimes due to enjoying lower costs of production or getting higher prices than Average costs, a firm may make profits

Stay even Analysis – what volume is required to offset a change in cost, price or other revenue factors

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Perfect Competition

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Traits of PC - No and size distribution of Sellers –

many small sellers – no seller able to exert a significant influence over prices

- No and size distribution of Buyers – no buyer able to exert influence over prices

- Firm is a price taker- Product Differentiation - nil- Entry and Exit - free

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Price taker Firm that has no influence over market

price and that thus takes the price as a given.

Price – taking behavior typically occurs in markets where firms produce identical, or nearly identical , products.

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Perfect Elasticity For the reason that a firm in a Perfect Competition ‘takes’ prices set at the industry

level, it encounters a fixed price and sells all its output at the same price - any effort to raise prices will result in zero sales: Therefore MR=AR or demand curve of the firm is just the price

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FIGURE 8.2 Demand curve Faced by a Competitive Firm

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When the products of all of the firms in a market are perfectly substitutable with one another – that is, when they are homogenous – no one firm can raise the price of its products.

Most agricultural products are homogeneous:

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Because product quality is relatively similar among farms in a given region, for example, buyers of corn do not ask which individual farm grew the product

Oil, gasoline, and raw materials such as copper, iron, lumber, cotton, and sheet steel are also fairly homogeneous.

{These days the advent of organics has changed the scenario a little bit. Traceability is called for - every product is traced to its grower –alternatively every farmers who is certified organic is able to sell his products duly labelled as organic. There is demand for a similar system for GM corn, maize and cotton}

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Free Entry and Exit This assumption, of free entry (exit),

means that there are no special costs that make it difficult for a new firm either to enter or to exit if it cannot make a profit.

As a result, buyers can easily switch from one supplier to another, and suppliers can easily enter or exit a market.

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Because firms can implicitly or explicitly collude in setting prices, the presence of many firms is not sufficient for an industry to approximate perfect competition.

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Conversely, the presence of only a few firms in a market does not rule out competitive behavior.

Suppose that only three firms are in the market but that market demand for the product is horizontal and the firms will behave as if they were operating in a perfectly competitive market.

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Marginal Revenue, Marginal Cost, and Profit Maximization

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The Basis for MR=MC The cost of production C depends on

the level of output. The firm’s profit, is the difference

between revenue and cost: π(q) = R(q) – C(q) Δ π / Δq= ΔR/ Δq – ΔC/ Δq=0Δ π / Δq = MR- MC=0ie Profit is maximized when MR=MC

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TR/TC method of determining Profit Maximization in the Short Run (Means firms make profit due to non entry by new firms): Slopes of TR and TC are the same at q* (profit maximizing output)

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Short – run Profit Maximization by a Competitive Firm

In the short run, a firm operates with a fixed amount of capital and must choose the levels of its variable inputs (labor and materials ) to maximize profit.

Figure shows the firm’s short – run decision.

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FIGURE 8.3 A Competitive Firm Making a Positive Profit: Notice Lost Profit (like Rt angled Triangle) is the gap between MC and MR: MC is like a supply curve above AVC The left part of MC is potential profit and the right portion is loss

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In the short run, the competitive firm maximizes its profit by choosing an output q* at which its marginal cost MC is equal to the price P(or marginal revenue MR) of its product.

The profit of the firm is measured by the rectangle ABCD.

Any lower output q1, or higher output q2,

will lead to lower profit.

Rules of MR to MC Sell more if MR>MC: sell less if

MR<MC

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Shut-Down Rule The firm should shut down if the

price of the product is less than the average economic cost of production unless the firm has incurred high sunk costs that it amortizes and treats it as fixed. In such a situation it should produce till price is above AVC

Average Economic cost Average economic cost is equal to

average total cost when there are no sunk costs but equal to average variable cost when costs treated as fixed are actually amortized sunk costs.

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Alternatively…… If revenue is less than avoidable

costs or equivalently price is less than average avoidable cost, then shut down

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Shut Down Rule Summed up If a firm does not have sunk costs

it shuts down at the point where Price < ATC When there are sunk costs (treated

as amortized Fixed cost) the firm shuts down when

Price < AVC

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A Competitive Firm incurring Losses

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FIGURE 8.5 The short-Run Output of an Aluminum Smelting Plant

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In the short run, the plant should produce 600 tons per day if price is above $1140 per ton but less than $1300 per ton.

If price is greater than $1300 per ton, it should run an overtime shift and produce 900 tons per day.

If price drops below $1140 per ton, the firm should probably stay in business because the price may rise in the future.

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Competitive Firm’s Short- Run Supply Curve

A supply curve for a firm tells us how much output it will produce at every possible price.

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We have also seen that average economic cost is equal to average total cost when there are no sunk costs but equal to average variable cost when costs treated as fixed are actually amortized sunk costs.

Therefore, the firm’s supply curve is the portion of the marginal cost curve that lies above the average variable cost curve.

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FIGURE 8.6 The Short – Run Supply Curve for a Competitive firm that has sunk costs

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In the short run, the firm chooses its output so that marginal cost MC is equal to price as long as the firm covers its average variable cost.

When all fixed costs are amortized sunk costs, the short-run supply curve is given by the crosshatched portion of the marginal cost curve.

Inventories that cannot be sold also represent sunk costs

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The Case of Texas Instruments In 1980s TI was selling computers for

$650. But competition from Commodore, Atari drove market prices downwards

By 1982 TI reduced its prices to $249 and still down to $149

TI VC was $100, so the firm continued to produce. By 1984 the price had to be reduced to $99. The firm stopped producing.

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The TI Case The firm had a stock of 500,000 unsold

computers TI got out of business by disposing the

stock at $49/piece. Why? TI had to face $100/unit COP before it

was produced but a sunk cost afterwards Thus TI was better off selling at $49 so long

as it was greater than the transportation costs (the costs that were still variable) of selling each unit.(inventory had to be forgotten as it was sunk- anything that covers your cost is fine)

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The Firm’s Response to an Input Price Change : Keep MC=Price: Reduce Production

When the price of its product changes, the firm changes its output level to ensure that marginal cost of production remains equal to price.

Often, however in the long run, the product price changes as prices of inputs change.

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FIGURE 8.7 The Response of a Firm to a change in Input Price

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When the marginal cost of production for a firm increases, the level of output that maximizes profit falls.

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The Effects of an Output Tax: On firm and Industry

We saw that a tax on one of a firm’s inputs creates an incentive for the firm to change the way it uses inputs in its production process.

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Now we consider ways in which a firm responds to a tax on its output.

To simplify the analysis, assume that the firm uses a fixed-proportions production technology.

If the firm is a polluter, the output tax might encourage the firm to reduce its output, and therefore its effluent, or it might be imposed merely to raise revenue.

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First, suppose the output tax is imposed only on this firm and thus does not affect the market price of the product.

We will see that the tax on output encourages the firm to reduce its output.

Figure shows the relevant short-run cost curves for a firm enjoying positive economic profit by producing an output of q1 and selling its product at the market price P1.

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Because the tax is assessed for every unit of output, it raises the firm’s marginal cost curve from MC1 to MC2 = MC1 + t, where t is the tax per unit of the firms output.

The tax also raises the average variable cost curve by the amount t.

The output tax can have two possible effects

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If the firm can still earn a positive or zero economic profit after the imposition of the tax, it will maximize its profit by choosing an output level at which marginal cost plus the tax is equal to the price of the product.

Its output falls from q1 to q2, and the implicit effect of the tax is to shift its supply curve upward .

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If the firm can no longer earn an economic profit after the tax has been imposed, the firm will choose to exit the market.

Now suppose that all firms in the industry are taxed and so have increasing marginal costs. Because each firm reduces its output at the current market price, the total output supplied by the industry will also fall, causing the price of the product to increase.

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FIGURE 8.18 Effect of an Output Tax on a Competitive Firm’s Output : Price is same – firm reduces output: Profit will come down

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An output tax raises the firm’s marginal cost curve by the amount of the tax.

The firm will reduce its output to the point at which the marginal cost plus the tax is equal to the price of the product.

Long-Run Elasticity of Supply The long-run elasticity of industry supply

is defined in the same way as the short-run elasticity:

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It is the percentage change in output (Q/Q) that results from a percentage change in price (P/P).

In a constant-cost industry, the long-run supply curve is horizontal, and the long-run supply elasticity is infinitely large.

In an increasing-cost industry, however, the long-run supply elasticity will be positive but finite.

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have a more elastic long run supply than will an industry that uses inputs in short supply

Because industries can adjust and expand in the long run, we would generally expect long-run elasticity’s of supply to be larger than short run elasticities.

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The magnitude of the elasticity will depend on the extent to which input costs increase as the market expands.

For example, an industry that depends on inputs that are widely available will have a more elastic long-run supply than will an industry that uses inputs in short supply.

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Figure 8.19 Effect of an Output Tax on Industry Output : Long run - Price goes up for Industry while output comes down

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An output tax placed on all firms in a competitive market shifts the supply curve for the industry upward by the amount of the tax.

This shift raises the market price of the product and lowers the total output of the industry.

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CASE STUDY The Short- Run Production of Petroleum

Products Suppose you are managing an oil refinery

that converts crude oil into a particular mix of products, including gasoline, jet fuel, and residual fuel oil for home heating.

Although plenty of crude oil is available, the amount that you refine depends on the capacity of the refinery and the cost of production. Output increases when there is a big jump in prices- this is done by moving from low cost to high cost refinery

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The Short Run production of petroleum products

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THE SHORT-RUN MARKET SUPPLY CURVE

The short-run market supply curve shows the amount of output that the industry will produce in the short run for every possible price.

Theoretically the industry’s output is the sum of the quantities supplied by all of its individual firms.

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Elasticity of Market Supply Unfortunately, finding the industry supply

curve is not always as simple as adding up a set of individual supply curves.

As price rises, all firms in the industry expand their output.

This additional output increases the demand for inputs to production and may lead to higher input prices.

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FIGURE 8.9 Industry Supply in the Short Run: S is sum of MC curves of individual firms : MC3 most efficient firm which starts Supply at P1 price

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CASE STUDY The Short-Run World Supply of Copper In the short run, the shape of the market

supply curve for a mineral such as copper depends o how the cost of mining varies within and among the world’s major producers.

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CASE STUDY Costs of mining, smelting, and refining

copper differ because of differences in labor and transportation costs and because of differences in the copper content of the ore.

Table summarizes some of the relevant cost and production data for the nine largest copper-producing nations

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CASE STUDY At relatively low prices , such as 50-55

cents per pound , the curve is quite elastic because small price increases lead to substantial increases in refined copper.

But at higher prices –say , above 75 cents per pound – The supply curve becomes quite inelastic because at such prices all producers would be operating at capacity.

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THE WORLD COPPER INDUSTRY (1999)

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The short-Run World supply of Copper

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The supply curve for world copper is obtained by summing the marginal cost curves for each of the major copper producing countries.

The supply curve slopes upward because the marginal cost of production ranges from a low of 50 cents in Chile and Russia to a high of 80 cents in Poland.

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For a review of consumer surplus,, where it is defined as the difference between what a consumer is willing to pay for a good and what the consumer actually pays when buying it.

Producer surplus sum over all units produced by a firm is the difference between market price of a good and marginal costs of production.

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Producer Surplus : PS=R-VC : Profit = R-VC-FCPS = Below P and above MC or ABCD. Why??Area under MC is Σ MC for (0 – q*) which is TC(q*)- TC(0) (or FC)= VCSpace between P and above MC is AR * q*- Σ MC or R - Σ MC where Σ

MC =VCSimilarly ABCD = (AR-AVC) X q* or R-VC

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FIGURE 8.12 Producer Surplus for a Market

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The producer surplus for a market is the area below the market price and above the market supply curve, between 0 and output Q*.

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Producer Surplus in the Long Run Note also that producer surplus measures the

difference between the market price a producer receives and the marginal cost of production.

Thus, in the long run, in a competitive market, the producer surplus that a firm earns on the output that it sells consists of the economic rent that it enjoys from all its scarce inputs that it has control on

Also when all factors are variable in the long run the PS=Profits

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Choosing Output in the Long Run In the long run, a firm can alter all its

inputs, including plant size. It can decide to shut down or to begin

producing a product for the first time. Because we are concerned here with

competitive market , we allow for free entry and free exit.

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P=MC is the Rule : Profit increased from ABCD to EFGD in long runThis happens when the market prices are High due to the demand factor despite easy entry constraints: If the price is at $30 the firm does not make profit

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Long –run competitive equilibrium in an Environment of continously high product price despite new firms entering

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Long run Equilibrium at $30: S shifts to right as more firms enter

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The long-run equilibrium occurs at a price of $30 as shown in (b), where each firm earns zero profit and there is no incentive to enter or exit the industry.

Firms having identical Costs To see why all the conditions for long-run

equilibrium must hold, assume that all firms have identical costs.

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Now consider what happens if too many firms enter the industry in response to an opportunity for profit.

The industry supply curve in figure (b) will shift further to the right, and price will fall below $30-say , to $25.

At that price, however, firms will lose money.

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As a result, some firms will exit the industry.

Firms will continue to exit until the market supply curve shifts back to s2.

Only when there is no incentive to exit or enter can a market be in long –run equilibrium.

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Firms having Different Costs Now suppose that all firms in the industry

do not have identical cost curves. Perhaps one firm has a patent that lets it

produce at a lower average cost than all other firms.

In that case , it is consistent with long –run equilibrium for that firm to earn a greater accounting profit and to enjoy a higher producer surplus than other firms.

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As long as other investors and firms cannot acquire the patent that lowers cost, they have no incentive to enter the industry.

Conversely, as long as the process is particular to this product and this industry, the fortunate firm has no incentive to exit the industry.

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Constant-cost, increasing-cost, and decreasing –cost.

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Supply Curves of Constant Cost, Increasing Cost and Decreasing Cost

Perfectly Competitive Industry

Constant Cost (CC) - Supply Curve Horizontal

Increasing Cost (IC) – Supply Curve Slopes up

Decreasing Cost (DC) – Supply Curve Slope Down

“ Reason for IC is heat on input price markets due to large number of firms entering” – case of BPO industry in India prior to economic crisis – talent pool shrinkage.

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Figure 8.16 Long-Run Supply in a constant-cost Industry

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In (b), the long-run supply curve in a constant-cost industry is a horizontal line SL.

When demand increases, initially causing a price rise (represented by a move from point A to point C), the firm initially increases its output from q1 to q2 as shown in (a).

But the entry of new firms causes a shift to the right in industry supply.

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Increasing-cost Industry In an increasing-cost industry, the

prices of some or all inputs to production increases as the industry expands and the demand for the inputs grows.

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This situation might arise, for example, if the industry uses skilled labor, which becomes in short supply as the demand for it increases.

If a firm requires mineral resources that are available only on certain types of land, the cost of land as an input increases with output.

Figure shows the derivation of long-run supply, which is similar to the previous constant-cost derivation.

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The industry is initially in equilibrium at A in part (b).

When the demand curve unexpectedly shifts from D1 to Q2.

A typical firm, as shown in part (a), increases its output from q1 to q2 in response to the higher price by moving along its short-run marginal cost curve.

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The higher profit earned by this and other firms induces new firms to enter the industry.

Increasing-cost industry Industry whose long-run supply curve is upward sloping.

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Long-Run Supply in an increasing-Cost Industry

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Decreasing-cost industry Industry whose long-run supply curve is

downward sloping.

Stay Even Analysis How to determine the volume

required to offset a change in costs, Price or other revenue factor.

Step even analysis tells you how many unit sales you can lose before the price increase becomes unprofitable

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Stay Even Analysis Let Profit 0 = P0Q0 – VC0Q0 – FC0

If we change price thus affecting Qty sold, our new profit equation is (assuming that fixed and variable costs do not change)

Profit 1 = P1Q1-VC0Q1- FC0

Given a new proposed P1 we want to find that Q1 that makes the two profit equations equal.

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Stay Even Analysis Thro algebraic manipulation we know

that Q1=Q0(P0-VC0)/P1-VC0

Say we are currently selling 600 units per week priced at Rs 20 per unity with VC of Rs 12/unit.If we reduced price by 10% how many more units would we need to sell to stay even on profit?

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Stay Even Analysis Plugging the values into the

formula results in a required new Qty of 800 units/week or an increase of 33%.If we knew the Ed we could tell how Qty would respond to the price change and decide whether the price change would be a good idea..

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Stay Even Analysis Suppose Ed is -2 then a 20% qty

increase will be there for a 10% price change . In this case then price decrease will not be a good idea because Qty will not change sufficiently

Elasticity would need to be approx -3.3 for the price drop to make sense.

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The End