# Microeconomics/Perfect Competition

Goals:
* To explain how firms decide how much to produce
* To explain how prices are determined
In order to achieve these goals, let's start with some definitions.

## Profit

The assumption is that the goal of the firm is to maximize profit -- to make as much money as possible.
$Profit=Revenue-Cost$
$Revenue=Price*Quantity$
There are 2 types of profit:
* Accounting profit = Revenue - Explicit costs
** explicit costs are actual payments for inputs
** wages you pay employees, cost of machines, other physical inputs
** firms report accounting profits
* Economic profit = Revenue - Explicit costs - Implicit costs
** implicit costs are the opportunity costs of non-purchased inputs
** extra money you could have earned, doing something else
** what the owner of a business could have been earning, working for another company
** return you could have earned by investing money in the stock market, instead of buying machines for your startup
    Accounting profit = USD 100,000 - 50,000 = 50,000
    Economic profit = USD 100,000 - 50,000 - 40,000 = 10,000
    Relationship between accounting profit and economic profit
    Accounting profit >= Economic profit
Economists (almost) always think and speak in terms of economic profit.
We also often refer to "zero profit". When we say, "zero economic profit" we mean that you are doing just as well with this business as with the next-best alternative.
If you are earning zero economic profit, you should stay in business.

## The Short Run (SR) v. The Long Run (LR)

* SR: Period of time during which you cannot change all inputs to production. At least one input is fixed.
** Ex. The size of your factory is fixed in the short run.
* LR: Period of time in which all inputs can be changed. All inputs can be varied in the long run.
** Ex. You can expand your factory in the long run.
We can redefine the SR and the LR in terms of costs.
* Fixed Cost (FC): Cost that does not change with the amount of output.
** Ex. The cost of land, machines, factories, your lease, your property taxes.
** No matter how much I produce, it costs me the same.
* Variable Cost (VC): Cost that changes with the amount of production.
** Ex. Amount spent on workers, electricity, etc.
If you increase your output, your VC increases.
    In the SR, at least one input is fixed, so at least one input cost is fixed. Therefore in the SR, FC>0.
    In the LR, there are no fixed inputs, therefore FC=0.
    Total Cost (TC) = FC + VC
Hint: Make a separate sheet of paper in your notes where you define all the costs and write the relevant equations.
For now let us focus on the SR.
This section is mainly concerned with macroeconomics.

## Production Function

The production function describes the relationship between all the inputs and the quantity of the output.
Ex. Suppose that you have a machine which originally cost USD 100. It has no resale value. You can hire workers at USD 20/hr each.
| L | Q |
| 0 | 0 |
| 1 | 4 |
| 2 | 9 |
| 3 | 17 |
| 4 | 20 |
| 5 | 21 |
Inputs include labor (L) and the machine.
The machine is a fixed input, and the number of workers varies according to output/quantity.
The marginal product of labor (MPL) is the amount by which the output changes if you change the amount of the variable input (the number of workers).
From the example: In the beginning, as L is increased, Q increases by an increasing amount. But as workers are added, the increase in Q decreases. Notice L(2) -> L(3) results in increase of 8 for the corresponding Q, while L(3) -> L(4) results in increase of only 3.

## Principle of diminishing returns

Suppose output is produced using 2 or more inputs and you increase one input while hold the other fixed. Beyond some point -- the point of diminishing returns -- output will increase at a decreasing rate.
Why is this? Because more and more workers are sharing a fixed quantity of other inputs. An example illustration is a cafe; for 2 to 3 employees, division of labor would be meaningful; one could take order, while the other could make the coffee at his table, and the 3rd employee could aid either one who is busier; but if the number of employee increases, say, to 10, while other things remain constant, there would not be enough table to even let the employees stand. Thus, at some point, additional employees do not add as much value as the ones before a certain number, which is called the point of diminishing return.
As such, this concept of diminishing returns explains why we can not grow all the world's crops on a single acre of land, just by adding enough fertilizer. Because at some point, the increase in output due to increase in input, the marginal increase, doesn't do as much.
The point of diminishing returns in the table above is at L=4. When you hire the 4th worker, he doesn't add as much to total output as did the previous worker.
Returning to the example, suppose you have a machine which costs $100. It has no resale value. You can hire workers at $20 each.
| L | Q |
| 0 | 0 |
| 1 | 4 |
| 2 | 9 |
| 3 | 17 |
| 4 | 20 |
| 5 | 21 |
Consider the example. Is this firm in the short run or the long run? Answer: the short run, because of the presence of fixed cost of $100 for the machine.
Long run is still subject to law of diminishing returns, but in some corporation examples, this may be due to the limit in the number of consumers. Just like the limited land and fertilizer example, there is a limit to the number of supermarkets, hamburger chains, bakery chains , white goods stores, consumer electronic chain stores and hardware stores that can be opened before there is not enough customers to cover the variable costs and per outlet fixed costs.
How much of a fixed input(s) is responsible for every q produced, on average?
Graph AFC (Average Fixed Cost)
$AFC={\frac {FC}{q}}$
On average, how much am I spending on the variable input(s)?
Graph AVC (Average Variable Cost):
$AVC={\frac {VC}{q}}$
Graph ATC:
$ATC={\frac {TC}{q}}=AFC+AVC$
If I increase or decrease my output slightly, how do my costs change?
MC looks like:
$MC={\frac {TC_{2}-TC_{1}}{q_{2}-q_{1}}}$
Marginal costs begin to increase when you add the 4th worker (point of diminishing returns)
Why? Beyond this point, each worker is relatively less productive, but you are paying each worker the same wage.
Graph the relationship between MC and MPL:
MC intersects AVC and ATC at their respective minimum points.
Why? Think of ATC as your GPA. Think of MC as your grade in this class.
* If your grade in this class is less than your GPA then your GPA will fall a little.
* If your grade in this class is greater than your GPA then your GPA will rise a little.
* If your grade in this class is equal to your GPA then your GPA will not change.
Similarly, when the cost of producing an additional good is less than the average cost, the average cost will fall a little.
When the cost of producing an additional good is greater than the average cost, the average cost will rise a little.
| Q of widgets | TC of widgets |
| 0 | 10 |
| 1 | 11 |
| 2 | 13 |
| 3 | 16 |
| 4 | 20 |
| 5 | 25 |
| 6 | 31 |
The AFC of producing 5 widgets is:
The AVC of producing 4 widgets is:
Example: You observe that at your current production of daikon radishes, the ATC is $1 and the MC is $2. What will happen if you increase production of daikon radishes by 1?
* MC will remain constant
* MC will decline
* ATC will rise
* ATC will decline
* Not enough information to say

## Firm Production Decision

Q: How much should a firm produce in order to maximize profits?
Goal of any firm is to choose the quantity $q$. b

## Profit Maximization Rule

Profit is maximized where $MR=MC$.
Profit maximization rule: Produce until the point where the change in revenue from producing 1 more unit equals the change in cost from producing 1 more unit.
Why?
Suppose MR > MC. If I produce 1 more unit, my revenues increase by more than my costs. Therefore, if MR > MC, producing more will increase my profit. If I can increase my profit by changing how much I produce, then when producing where MR > MC can't be profit-maximizing.
Suppose MR < MC. If I produce 1 less unit, my revenues decrease by less than my costs decrease. Therefore, if MR < MC, I can increase profit by decreasing output. If I can increase profit when MR < MC, then choosing q such that MR < MC can not be profit-maximizing.
So, in order to maximize profit, I must choose a quantity q such that MR = MC.
MR = MC is an equilibrium in the sense that it is the only place where there is no incentive to change the production level.
This rule, the profit maximization rule, is just an application of the marginal principle (MB = MC).
Why? This MB of producing an extra unit is the extra revenue you get. MR is the MB. So the 2 statements are equivalent. The marginal principle is more general, and the profit maximization rule is specific to the firm production decision.

## Perfect Competition

Now let us apply the profit maximization rule to the specific case of perfect competition. First, list the characteristics of a perfectly competitive firm.
Characteristics
* Homogeneous: every firm produces exactly the same good. Consumers can't tell any difference between what one firm produces and what another firm produces.
* Many firms: each firm represents a very small part of the overall industry.
* Price taker: any individual firms's decision of how much to produce will not affect the market price. This is a result of the first 2 characteristics.
* Free entry and free exit: There exist no barriers to prevent firms from entering or exiting a certain market in the long run. This implies zero economic profits in the long run.
Very few firms or markets would satisfy these characteristics. Closest example of a perfectly competitive market is agriculture
* a particular variety of wheat is the same no matter where it is grown
* there are many small farmers, so that whether or not Farmer Bob produces an extra 5 units does not affect the market price
Despite the rare and extreme nature of perfect competition, it provides a useful baseline case.
Graph the typical representative perf. comp. firm next to the industry to which it belongs. Show how price is determined in the market and then guides the individual firm's decision.
Profit-maximization rule: Choose q such that MR=MC.
q* = that amount which a perfectly competitive firm will produce given P* in the market.
Revenue = Pq*

## Profit Maximization in Perfect Competition

From the assumption of perfect competition, any individual firm's decision of how much to produce does not affect the market price. Therefore, P = MR for an individual firm ,( because it is known that price is constant for any quantity produced, and marginal revenue is the price of producing one further unit of quantity, and price is constant ; price is constant because price does not increase at any quantity demanded because most other companies will still sell at the same price and no one can compete at a higher price).
Remember that profit maximization rule says to set q such that MR = MC ( because of the law of diminishing returns, when MC is rising and has reached MR, MC will be greater than MR for any more units, or the marginal profit which is MR - MC will be less than zero ).
Since P = MR and the firm sets MR = MC, we can write that in perfect competition,
Set q* such that P = MC ( because for every unit before the qth unit, there was a net profit of P-MC > 0 for each unit , because MC was rising and has to be less than the MC at MC = P ).
On the graph, find the point where the price line intersect the marginal cost curve. Then look at the horizontal axis to determine which q corresponds to that point. This is the firm's profit maximizing quantity.

## Cost and Price Minimization in Perfect Competition

There is also an equalitarian, non-corrupt side of perfectly competing market that suggests transparent market competition is good for the consumer: as each company seeks to to produce the last unit where the marginal cost is just less than the price, and therefore have produced as many profitable units as possible, so they will try to sell at a price that is the lowest and still profitable , which is above the average total cost, and they will try to price at a quantity above the minimum average total unit cost. If they sell below the ATC , they can cover variable but not fixed cost, and so they try to reduce costs. If they sell above the minimum ATC, their competitor will sell more and they will try to increase efficiency to match the minimal ATC. So this brings up the Utopian vision that in a perfectly competing market, the fair price is that buyers get the same price as the minimum unit cost which covers all the cost of production including the fair minimum costs for labour and management , and no more. And producers sell at a maximum quantity where their last units of production still turn a profit. The lowest prices and as much as possible while letting the adequately efficient producer survive. P = MC = minATC. Economic heaven!

## Case 1: Positive Profits

Profit > 0
Revenue > Total Cost
Intuitive example: On average, it costs $5 to make each unit. Can sell each unit for $7. Must be making a profit.
ATC(q*) = how much it costs you on average to produce each unit, given that you are producing q* units.
Revenue = p q* = A + B
TC = B
Profit = Revenue - TC = A
Note: it is a common mistake to identify q* as the q where MC = minimum ATC. This is wrong! This quantity does not generally maximize profit. It maximizes profit per unit.
However, in the LR, because of free entry and exit, profit will equal zero, and ATC will be minimized. This is a feature of perfect competition. But the firm is not trying to minimize ATC -- it tries to maximize (TR - TC). ATC is only minimized indirectly in the long run.
Should a firm stop producing (shut down) if profits are negative? (Recall this is in the SR.) Answer: It depends.
This an old joke about economists. They can never give a Yes or No answer to a question. They always say, "It depends." That isn't really true in general, but in this case, "It depends," is the correct answer.
Note: stopping production does not mean going out of business.
Ex. Tourist businesses might shut down in the off-season.
Why? Whether or not you are producing anything, in the SR, you still have to pay your FC.
You should stop producing only if you are losing more money by producing than by shutting down.
We need a rule. Let's derive it.
    Loss > FC
    TC - Revenue > FC
    FC + VC - Revenue > FC
    VC - Revenue > 0
"VC > Revenue
That is, shut down if you can't afford to pay your workers. If you continue producing, your profit will be negative. But if you shut down, you limit your losses to the amount of FC you have to pay. If VC > Revenue, you'd lose even more than FC by staying open. In general, if you are losing money, you have to decide whether shutting down or staying open will minimize your losses.

## Case 2: Negative Profits: Stay Open

You lose money because P < ATC
But since P > AVC,
P > AVC
P*q > AVC*q
Revenue > VC
So you are able to cover the cost of your labor inputs, and pay some of your fixed cost as well, by staying open.
Revenue = B + C
TC = A + B + C
Negative profit = A
VC = C
FC = A + B
If you keep producing, lose A
If you stop producing, lose A + B
Example: P* = 8. Calculate loss, fixed cost, and explain why the firm should keep producing. This is the mini we had in class. Your answer can be showing the amount of VC, FC, and calculating profits for the case of staying open and for shutting down.
For fixed costs such as capital, it then depends on the after-tax cost of capital resource over the life of the capital resource, because if say the resource has a life of 10 years, and it takes 8 years to cover the replacement cost after tax deductions for depreciation, then it is still profitable to stay open for 10 years.
If there is a recurring fixed cost , then if the fixed cost minus tax deduction exceeds the revenue less variable cost, then money is being slowly lost over the long term.

## Case 3: Negative Profits: Stop Production

Negative profits:
Stop production if:
VC > Revenue
q * AVC > P * q
AVC > P
Shut down if P < AVC on the graph.
Graph the perf. comp. firms costs, with P below the AVC curve.
Revenue = C
TC = A + B + C
Negative profit = A + B
VC = B + C
FC = TC - VC = A
If you keep producing, you lose A + B
If you shut down, you lose A
So you lose less money by shutting down.

## Derivation of the Firm's Supply Curve

We have shown that a firm will keep producing as long as P >= AVC.
Suppose P < AVC. Then q* = 0
    If P = AVC then q > 0
    If P > AVC then q > 0
So for all P >= AVC, there exists a certain q that a firm will supply. The firm supply curve is the MC at or greater than AVC.
By the Law of Supply, as P increases, Qs increases.
Why? Firms produce more. Firms that have stopped producing, but haven't gone out of business, may start producing again.
The elasticity of supply depends on the MC curve.
    An elastic S curve means that a firm can increase its Qs without a very large increase in MC.
    An inelastic S curve means that MC increases sharply for an increase in the Qs.
Market Supply: Add up all the firms' S at every P.