We will determine how the firm derives it’s supply curve when they know production and costs in a perfectly competitive market.

Three assumptions of a perfectly competitive market place.

1.  Price Taking:  Since there are many firms in the market so many firms no one firm can influence price.  Thus each individual firm takes the price that is established in the market as the price they will charge for the product.

2. Product Homogeneity:  When all the products are the same, that is they are perfect substitutes for each other.

3.  Freedom of entry and exit: Firms are free to enter and leave the market at any time.  This does not mean it is actually free of costs to enter the market it just means that the costs associated with entering a market are not so large that it prevents people from doing so.

While we assume that firms maximize profits it is important to recognize that managers of firms also try to achieve other goals.  Some of these goals might be revenue maximization or growth or dividend payments rather than profit maximization.  This often leads to the principle agent problem.  That is the owners interest (profit maximization) might not be the interest of the agent (management).  However, in the long term profit maximization is the goal of a business even though in the short run managers might be distracted from this goal.

Profit is total revenue minus total cost or

p(q) = R(q) –C(q)

where profit, revenue and costs all depend on the output produced by the firm.

Profit is maximized when the amount between total revenue and total cost is the greatest.

Insert Figure 8.1 here.
 
 
 
 
 
 
 
 
 
 
 

The revenue curve R(q) shows that a firm can sell more output by lowering price.
Note that as output increases in the beginning the price is higher which is why revenue is rising faster thus profit goes up, but then eventually they have to lower price to continue to sell more output but then revenue doesn’t increase as much because the price is getting smaller.  Thus we see slope gets smaller and profit starts to decline.  The slope of R(q) is marginal revenue.  Which is the extra revenue of selling one more unit of the good.

The total cost curves C(q)  slope shows marginal cost the additional cost of producing one more unit of output.

Notice how profit increases then is maximize at output level q*.  Notice that the line AB is the greatest distance between cost and revenue.  Also recall that the slope of total cost and total revenue is marginal cost and marginal revenue.  If you look at the slope of the dotted lines tangent to points A on R(q) and B on C(q) you will see they are parallel and slopes of parallel lines are equal thus MC the slope of C(q) equal MR the slope of R(q).

Thus profit is maximized when MR=MC.

Explain in words why profit is maximized when MR=MC.  To do so explain what happens to profits if they are not equal.
 
 
 
 
 
 
 

Prove algebraically that profit is maximized when MR=MC.
 
 
 
 
 
 
 
 
 
 
 

Show and explain why the demand curve faced by a single firm in a competitive market is horizontal. Also explain why MR average revenue and price are all the same.
 
 
 
 
 
 
 
 
 
 

Insert Figure 8.2 here.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Since MR = P  the profit maximizing rule can be expressed as:

MC(q)=MR(q) =P

Now that we know how the competitive firm gets the price it charges we have to devote the rest of this chapter to how output is determined.  Since firms will maximize profit we now want to see the output level that allows the firm to maximize profit.

Insert figure 8.3.
 
 
 
 
 
 
 
 
 

Notice profit is maximized when MR=MC at point A producing an output level of 8 units.  Also note that MR =AR =P

Explain why 7 units of output will not maximize profit.
 
 
 
 
 

Explain why producing 9 units of output will not maximize profit.
 
 
 
 
 
 

In figure 8.3 we see the profit per unit of output produce is the line segment AB.  We know this is profit because the average total cost of producing 8 units of output is $32 (point C on vertical axis).  But the average revenue associated with each of those 8 units of output is $40 (point D on vertical axis).  thus there extra profit of $8 per unit of output and since there are 8 units of output there is 8*8 of profit above what is necessary to maximize profit.  This is often called economic profit or excess profit.  It is denoted by the rectangle ABCD.  This economic profit occurs because the price where this firm maximizes profit is high enough to recover all of the costs associated with producing 8 units of output.  One of those costs are opportunity cost of the entrepreneur or what was referred to a normal profit in your principles class.  This amount of extra profit does not always occur.

Insert Figure 8.4 here.
 
 
 
 
 
 
 

The only difference between figure 8.4 and 8.3 is that 8.4 has more fixed costs.  Thus the difference between ATC and AVC is much bigger in 8.3.  Price and everything else is the same.

Notice in 8.4 profit is maximized at point A and q* output but this time the price is not high enough to recover all of the fixed costs.  In fact since fixed costs are shown by the line segment BE we see BA amount of fixed costs are not recovered.    However, the firm is recovering AE amount of fixed costs.  It is loosing BA.

The question is what should the firm do?  Often we read in the newspapers about companies that are loosing millions of dollars and yet they stay in business.  One question we often ask is how can they lose so much money and stay in business?  Firms maximize profits but if they can’t make a profit (like in figure 8.4) then the best they can do is minimize losses.

In figure 8.4 if this firm goes out of business they still have to pay their fixed costs BE.  So BE would be what they lose.  But if they stay in business they lose BA.  Since BA<BE it pays for them to stay in business.  They are able to recover all there variable costs q*E and part of their fixed costs AE.  In figure 8,4 the rectangle ABCD shows the firms total loss, which is less than the total loss CBEF if they shut down.

What is interesting is how sunk costs come into play here.  Remember sunk costs mean there are no opportunity costs for the resources.  This is very rare.  Nevertheless if fixed costs are actually sunk costs then the firm should just shut down when they are operating at a loss.  But it is not common for all fixed costs to be sunk costs thus the firm will continue to operate while minimizing their losses.

Explain why and when the firm should shut down (assume no sunk costs).
 
 
 
 
 
 
 
 

Insert Figure 8.6 here.
 
 
 
 
 
 
 
 
 
 
 
 

We will now show that the positively sloped supply curve that we are so familiar with is simply the marginal cost curve above the minimum average variable cost curve.
When the book talks about sunk costs being amortized they are simply saying that the sunk costs of the firm, will be valued as a cost just as if they were fixed costs.

Profit is maximized whenever, MC=P.  So if the price is P₂ the firm will maximize profit and produce an output level of q_2.  Now suppose the price in figure 8.6 drops to P₁.

Explain how the price the firm charges for the goods it produces can drop.
 
 
 

At P₁ profit is maximized where MC = P₁ and the output that allows the firm to maximize profit is q₁.  Now suppose the price drops to P (again you should be able to explain why the price might fall to P).  Profit is maximized where MC = P, the output level allowing the firm to maximize profit is not shown in the diagram but you can see that it would be less than q₁.

What will the firm do if Price drops below P in figure 8.6?
 
 
 
 

We know the supply curve tells us the relationship between price and quantity supplied and we know that there is a positive relationship.  Note however, we just showed the relationship between different prices and the quantity supplied by the firm at those prices.  Thus the supply curve is the Marginal cost curve above the minimum point of the average variable cost curve.

Recall that the reason the MC curve goes down and then up is because of the law of diminishing returns.  In particular once diminishing returns sets in MC starts to rise.  Since MC is the supply of labor therefore the law of diminishing returns also explains the upward slope of the supply curve.

Insert Figure 8.7 here.
 
 
 
 
 
 
 
 
 

It is possible that the input price of producing a good and the product price both change. Figure 8.7 shows how the firms output decision (which is based on MC=MR profit maximizing condition) is affected by a price change in a input.

In figure 8.7 the market established a price of $5.  MC₁ is the original MC and profit is maximized at the output level q₁.  If the price of an input goes up costs increase including MC, which rises to MC₂.  The new profit maximizing output level is now q₂ <q₁.

Explain what would happen if the firm continued to produce q₁ instead of q₂ when the input price went up.

notes added monday night november 17

The short run supply curve of the firm is the MC above the AVC curve, and since the horizontal sum of all the individual firms supply curves are the MC above AVC it includes the lowest price associated with the individual firms MC that is above AVC.

Insert figure 8.9 here.
 
 
 
 
 
 

Notice there are three firms and the market supply curve is the horizontal sum of all three including the third firm who has a MC associated with P₁.  It is easier to just draw the industry supply curve as a smooth upward sloping curve.
 

The price elasticity of market supply tells us how sensitive quantity supplied is to market prices.  It is the percent change in output divided by the percent change in the price.

A perfectly elastic supply curve, horizontal, tells us any reduction in price will have firms decide not to supply any of the goods.  This is because MC is constant and if price falls the firms will close down.

A inelastic supply curve tells us that no matter what happens to price the firms can’t increase output in the short run because all the plants are being fully utilized.  They can only increase output in the long run.

We discussed in chapter 4 that consumer surplus is the difference between what a consumer is willing to pay for a good and the amount they actually pay.  Producer surplus uses a similar concept.

Insert Figure 8.11 here.
 
 
 
 
 
 
 
 
 
 
 

What is producer surplus?
 
 
 

Producer surplus can be measured as the area above a producers supply curve but below the price.

Insert figure 8.12 here.
 
 
 
 
 
 
 
 
 
 

Figure 8.11 is the short run producers surplus for one individual firm, versus figure 8.12 which is producers surplus for the market (all the firms combined).

Profit is maximized when P=MC which occurs at q*.  The surplus for the producer is the difference between the market price P and the MC associated with producing each unit of output.  If you add this (sum) for all units of output we see it is the yellow area under the firms horizontal demand curve in figure 8.11 from zero output to the profit maximizing output of q*.

Since fixed costs are constant in the short run the sum of all the marginal costs have to equal the sum of all the variable cost.  Thus figure 8.11 shows producer surplus as the area ABCD also the variable costs associated with each level of output from q to q*.  Note how this is simply the revenue the firm makes OABq* minus variable costs ADCq*.
 

We will now go through the long run dynamics of how a competitive market place determines the long run price.  Several things to remember;
Freedom of entry and exit.  Firms are free to enter or leave the market.

Also remember the difference between accounting profits and economic profit.  This is very important.

What are the differences between accounting and economic profit?
 
 
 
 
 
 
 
 
 
 
 
 
 
 

What is zero economic profit telling us?
 
 
 

Insert figure 8.13 here..
 
 
 
 
 
 
 
 
 
 
 

Note this is the long run cost for a firm.  It also includes the short run costs.  The market established a price of $40 which is P=MR and horizontal.  This is so for both long and short run because the firm is a price taker from the market.

Suppose short run costs are SAC and SMC and this firm is very well run thus those costs are low enough to make positive profits.

Explain how you know profits are maximized and positive at the output level of q₁
 
 

Since LAC is declining in this range we know the firm in the long run is experiencing economies of scale and will experience these until the output level of q₂ is reached.

As this firm whose costs are represented by SAC and SMC what will you do as a result of this profit you are making? Explain why?
Remember the profit you are making is above the normal profit.  That is you are making more than you can in other investments.

In the long run profit is maximized where long run marginal costs equals price.  If they produce at an output level less than that (q₂) we see MR>MC and the firm should expand because in doing so they increase profit.  Also if produce beyond q₃ MC>MR and the firm can increase profit by producing less since it will save more in costs than what they lose in revenue.

Profit depends on price the lower the price the less profit.  In this case if the price dropped below $30 the firm would no longer stay in business and will close down because it can’t recover its long run costs.

Now the dynamic model becomes fun when we see how it works.  It is of course based on the assumption that all firms are free to enter and leave the industry.

Notice in figure 8.13 that the firm is making economic profit when the price established by the market is $40.  Since there is economic profit the firm is making more than alternative returns on their capital investment.  Other firms see this economic profit and decide to enter the market also since the returns are higher than what they can earn elsewhere.  When they enter the market the supply of output in the market increases.

Insert Figure 8.14 here.
 
 
 
 
 
 
 
 
 
 
 

Notice when new firms enter the market Supply increase and the price is bid down to P₂. This is the new market price, which the original firm now charges.  Since the cost of production is the same the excess profit is disappearing as new firms enter.  Eventually, the price drops until the MR=P at the minimum LAC for the individual firm.  At that point the firm is making just a normal profit and there is no longer any reason for new firms to enter the market.

We will now discuss how the Industry derives the long run supply curve.

Since price is always changing in the long run as new firms enter and exit the industry it is impossible to sum all the individual firms supply curve like we do in the short run.  We don’t know which firms are that are in the industry because they are always leaving and entering.

The shape of the long run supply curve is determined by the type of input price structure of the industry.  That is it depends on what happens to the costs of the inputs used to produce the outputs when output goes up in the industry.

If the input prices used to produce additional output do not go up then we say it is a constant cost industry.  If the input prices go up then we say it is a increasing cost industry and if input prices fall then we say it is a decreasing cost industry.  Remember in all three situations output expands and to produce that output firms need to hire workers and/or use more capital etc.  When they hire more inputs, depending on the type of industry, the costs of those inputs either stay the same, go up or go down.

Long run supply in constant cost industry

Insert figure 8.16 here.
 
 
 
 
 
 
 
 
 
 
 
 
 

Suppose the initial short run market supply and demand is S₁ and D₁ and the price established by the market is P₁. Equilibrium in the market is at point A.

If you look at diagram 8.16a, which is for one firm in the market, long run equilibrium occurs at the minimum AC.  There is no longer anyone coming in and out of the market since there are no excess profits.

The firm represented by figure 8.16a is associated with the price P₁in the industry.  The industry will supply Q₁ units of output at P₁.  Thus point A is one point on the long run supply curve.  The individual firm produces q₁ units of output, which is some portion of the industry output Q₁.

Suppose something happens and the demand for the product in the industry increases to D₂.  This might occur because income went up, or the good became more popular, or any of the reasons that cause demand to increase. Notice that equilibrium price rises to P₂. The individual firm takes the price that the market establishes and charges that to its customers and producers q₂ units of output in order to maximize profit.  The firm is now making economic profit, which is something it was not doing when we first started the analysis.

This increase in price has occurred for all firms in the market. Thus, all the firms increase output. Additionally new firms realize that there is excess profit and that their capital can be earning more than it has been earning elsewhere and decide to enter the industry, which further increases output.  This increase in output is shown in the industry by the supply curve increasing to S2.

Here is what is very important in this dynamic model.  Whether we are a constant, increasing or decreasing cost industry the analysis is all the same up to this point.  That is long run supply increases.  The difference between the different cost industries is how much supply increases by.

In a constant cost industry, which tells, us that as output expands and firms need more inputs the price of those inputs do not go up.  This is not saying it is not costing more to produce more output because it is, what this is saying is that the input price does not go up as firms use more inputs.  Thus wages of a worker will stay the same as firms increase output.  This can happen because maybe there is some unemployed workers who are happy to get a new job so don’t have to raise wages to get them to work. The new equilibrium price with new demand D₂ and new supply S₂ occurs at point B and price goes back to P₁ and quantity is Q₂.   This shows the relationship between output and price and thus is another point on the long runs supply curve.  Connecting these two points AB gives us the horizontal long run supply curve in a constant cost industry.

Increasing cost industry long run supply curve.

In an increasing cost industry when output expands because of the increase in demand the firms need more inputs and this time (unlike in constant cost industry) the input prices are bid up.

Insert Figure 8.17 here.
 
 
 
 
 
 
 
 
 
 
 

Everything is exactly the same as what we just did.  Initial equilibrium occurs at the firm’s minimum point on SAC curve making a normal profit.  Demand increased, for some reason, and the price goes up. The individual firm is now making excess profit.  They expand as do all the firms that are making excess profit and new firms enter the market because the returns on their investments are greater in this industry.  This increase in output is shown by the industry supply curve in figure 8.17 increasing.

Because this is an increasing cost industry when output expands the cost of the inputs to produce the additional output also goes up.  So now the individual firm in diagram 8.17a goes up to AC₂ and the associated MC₂ curve.  In long run equilibrium the new equilibrium price of P₃ has to equal the minimum point on the firms short run AC curve which occurs at the same output level q₁. Because of new firms entering the market there is no longer any economic profit.  The market supply increases to S₂, which shows the price to be P₃.  Since input prices went up and average costs also went up for each unit of output supply doesn’t increase as much and when we connect the two new equilibrium points the long run supply curve is now positively sloped in a increasing cost industry.
The supply doesn’t increase as much because the more expensive input prices make the expansion less profitable and some firms decide not to enter the market who would have if the input prices remained the same.

You should be able to explain the entire process for a decreasing cost industry.  That is show that a decreasing cost industry will have a negatively sloped long run supply curve.

Stop on page 280 .