Chapter 8 - Profit maximization

Question 1

What does a cost curve describe?

Answer 1

A cost curve describes the lowest cost for each level of output. It is based on the expansion path from inputs. Therefore, the cost curve will contain points where a cost optimal combination of inputs are entered.

Question 2

What is the fundamental problem of chapter 8?

Answer 2

Chapter 8 concerns mainly about how much we should produce. Given a cost curve, what level of output should we aim for?

We obviously want to choose a level of output that maximize our profits

Question 3

What are the assumptions that the perfect competition model relies on?

Answer 3

1) Price taking

2) Product homogeneity

3) Free entry and exit

Question 4

What is meant be “price taking”?

Answer 4

Price taking is basically accepting that the price is given. Therefore, a firm cannot do anything about it. It doesn’t make sense to increase price, as it will destroy sales (competitive market).

Price taking is something that occurs in perfectly competitive markets.

it is easy to think that a firm could lower price to sell more, which is true in real life, but not in the theoretic model. We assume that firms sell all that it can produce. Therefore, we limit our analysis to “the optimal amount of output to sell”. The actual selling is of course a different subject.

Question 5

Why is the assumption of product homogeneity important?

Answer 5

Product homogeneity implies that there is a single market price. If products are different, we are not actually pricing a single product, but many several. In such case, it is difficult to say anything about the market price.

Question 6

What is required to be able to group several products under the same “market price”?

Answer 6

Market price involving several products requires product homogeneity.

Question 7

Name an example of industry that does not have free entry and exit

Answer 7

Pharmaceuticals.

Question 8

When we say that a firm is facing a demand curve, what are we referring to?

how does this relate perfectly competitive markets?

Answer 8

We are referring to the relationship between the quantity demanded by consumers (from the firm) at the various price levels that the firm might set.

In a perfectly competitive market, the demand curve that a firm face will be horizontal. This means, consumers are willing to by “any” amount of the good, as long as it is at the price level indicated by the curve/line. This means that the price doesn’t change, as there is no incentive to do so. Why? Because firms sell all that it produce. This is fundamental in this model.

Question 9

In real life, is perfect competition normal?

Answer 9

No. Agriculture is generally accepted as perfectly competitive. However, this is not common.

We have cases of highly competitive markets though. In such cases, the firms face highly elastic demand curves. This means, a small change in price would lead to a very large change in quantity demanded.

Question 10

For any firm, what is the profit?

Answer 10

Profit is defined as the difference between total revenue and total costs.

Profit = R(q) - C(q) = Pq - C(q)

We usually say pi(q) = R(q) - C(q)

Question 11

Picture the revenue curve R(q).
Why is it curved? As opposed to what…?

Answer 11

As opposed to being a straight line.

It curves because of the natural relationship between prices and output. If we want to increase output, we might have to reduce the price. This means that the revenue will start to slow down as the output level q reach a certain value. It also means that at some output, revenue will actually start to decrease. This means that producing more units will NOT be beneficial, as we will have to keep decreasing price to increase the output.

The point is that when we want to increase output, we will have to decrease price. If it happens to be so that the price decrease is “worse” than the gain in demand, our total revenue will drop. This would be shown by a negative slope on the revenue function.

Long story short, revenue is dependent on the price per unit and the number of units. The curved revenue function (usd on Y, output on X) indicates that higher output will decrease the price.

Question 12

What is marginal revenue?

Answer 12

Marginal revenue is the additional revenue we get by selling one more unit of output.

Marginal revenue is also the slope of the revenue function. This means, if the slope is negative, we would actually loose money/revenue. NB: We would loose total revenue. This does NOT MEAN that prices are negative. It means that the change in price (decrease in price) is more significant than the increase in demand.

Before price change: p0 * q0 = R0
After price change : p1*q1 = R1.
If q1 == q2, we would obviously get R0 > R1. Then we would make less revenue than previously.

Question 13

What is marginal cost, and how can we find it?

Answer 13

We can find it by differentiating the total cost curve. The total cost curve is given as costs in USD on Y, and level of output at X.

Marginal cost is the additional cost required to produce an extra unit. It is the slope of the cost function.

Question 14

Why does the cost curve “curve”?

Answer 14

The cost function is curved, as opposed to a straight line, because of 2 large factors:

1) At some point, our business will experience economies of scale. Therefore, costs will be reduced compared to output.

2) At some point, much later than previous point, our business has become so big that we are struggling to find raw materials. In such case, the price of them materials will increase. this means higher costs for us.

Question 15

What can we say about the total cost curve at the point of zero production?

Answer 15

We know that it will be positive with some offset. Why? Because of fixed costs. The revenue curve will start at (0,0) but the cost curve will start at (0, c) where c is the fixed costs.

Question 16

What is the profit maximization rule that applies to all firms, regardless of the competitiveness of the market they operate in?

Answer 16

The rule is that profits are maximized when marginal revenue is equal to marginal costs.

(Assuming the cost curve never slopes down (negative) with increased output, and revenue curve behaves normally)

Intuitively, this makes sense. If we are in this point, adding another unit will involve more costs than revenue. The cost of producing the unit is more than the revenue. We would never do this.
Simultaneously, reducing the output would mean giving up a unit that carry more revenue than costs, which means giving up money.

Question 17

How does the revenue curve look like in a perfectly competitive market?

Answer 17

Considering the fact that suppliers are price takers, the increased (or decreased) level of production would not impact that price in any way. Therefore, the slope would never change. This means that the revenue curve would be a linear function. Therefore, the level of profit maximization would be at the point where the slope of the cost funciton is equal to the slope of the cost function.

Question 18

What is the difference between market demand curves and the demand curves faced by individual firms?

Answer 18

In perfect competition, the demand curve faced by an individual firm would be a horizontal line. However, this would NOT be the case for the market demand, even though the market is perfectly competitive.

Firms in perfectly competitive markets are price takers.

the market demand curve shows how much of a good the market (all consumers) would consume at each possible price.

The demand curve facing the indicvidual firm is horizontal because the sales have no impact on the price.

Question 19

For a firm in a perfectly competitive market, what is the average revenue curve?

Answer 19

The average revenue curve would be equal to the demand curve (horizontal line) because of the competitiveness.

It would also be equal to the marginal revenue curve.

All is equal to the price

Question 20

What is the general rule of profit maximization for competitive firms?

Answer 20

It is still MR = MC, but now we have informaiton on the MR, which would be the price.

Therefore, competitive firms maximize profits when the marginal cost is equal to the price that is given in the market.

Question 21

Recall short run restrictions

Answer 21

In the short run we consider capital fixed. This means, we concern ourself with choices regarding output levels whenever we cannot change larger pieces of infrastructure.

Therefore, the question of profit maximization in the short run becomes “how much should be produce, given prices of variable inputs like labor and materials, and the price we get by the market”.

Question 22

In perfect competition, how does the marginal revenue curve look like?

Answer 22

Flat line, horizontal. Same as average revenue. Same as the demand curve.

Question 23

If we have the curve for marginal revenue and the curve for marginal costs, how do we find the profit maximizing output level?

Answer 23

the intersect point between them. When marginal cost is equal to marignal revenue.

Question 24

Why can we not always naively use MC=MR as rule for the profit maximizing output?

Answer 24

Because the marignal cost curve might intersect the marginal revenue curve at multiple points. the key point here to know whether the marginal cost curve is rising or not beyond the point. The whole point is to choose a point where adding another unit brings more costs than revenue. Never forget this.

Question 25

Let us say we are at the point where MR = MC and MC is rising beyond this point. Do we make money?

Answer 25

Impossible to say. We only know that at this point, we are making the best out of our current situation. However, we cannot say whether or not we are actually making money. it is all about the fixed costs.

Regarding variable costs: If we know that we have reached an output level where we have gone from lower marginal costs, to higher and then to the point where marginal revenue equals marginal costs, we know that the price is sufficient to cover variable costs (marginal as well). However, the fixed costs may be very large or very small, we dont know.

Question 26

When is a firm losing money accoridng to microeconomic theory?

Answer 26

A firm is losing money if the price is lower than the average total costs at the output level corresponding to profit maximizing.

Question 27

When should a firm shut down, according to short run theory?

Answer 27

If the firm is losing money (Price is less than average total cost at profit maximizing output level) and there is little hope of improving conditions, the firm should shut down. It doesnt matter if price is larger than variable costs, as the maximized profit will not be enough to cover all the costs.

Question 28

if price is larger than average variable costs, but the firm is losoing money, should it shut down?

Answer 28

Depends. If the future looks bright (new tech etc) then obviously no.

However, the point is that, if we are producing at the profit maximized output level, we physically CANNOT make more money (unless external conditions change). Therefore, we will lose money by doing it. Therefore, we should quit.

Question 29

What does a supply curve for a firm tell us?

Answer 29

A supply curve for a firm tells us how much the firm will/is willing to produce at each price.

Question 30

If price is below average variable cost, should we shut down?

Answer 30

Yes

Question 31

What is the supply curve of the firm as defined by marginal curves?

Answer 31

Since a firm will shut down business if price is below average variable cost, we can say the following:

The firm’s supply curve is the portion of the marginal cost curve for which marginal cost is greater than average variable cost.

We dont care about the part of the marginal cost curve that is beneath the average variable cost curve, because the firm will produce nothing at these levels.

THerefore, we can plot average variable cost curve and marginal cost curve, mark the intersect point, at we get the supply curve of the firm.

This basically means that the supply curve is the same as marginal cost curve (at some interval). This makes a lot of sense, because we are always looking for the point where marginal cost is equal to marginal revenue. Since marginal revenue is a horizontal line, and also represent demand curve that the firm face, the intersect between these two curves will mark the output level we want to produce at.

Question 32

How can we derive the short run supply curve?

Answer 32

We utilize the fact that firms are ALWAYS looking to maximize profits. Therefore, regardless of where we (the firm) we be on the supply curve, we KNOW that marginal cost is equal to marginal revenue.

We dont know the price level, but that does not matter. As long as we know the marginal cost curve, we have the supply curve. This is because the marginal revenue curve will intersect the marginal cost curve to profit maximize, so we can treat the entire marginal cost curve as a supply curve.

however, there is no point in keeping the part of the marginal cost curve (supply curve) where we are shutting down the business. this happens at the interval where marginal cost curve is beneath the average variable cost. Why? Because if we were to regard that interval, then PRICE would have to be beneath it as well. IF this were the case, we would lose money (variable cost higher than price) which we never want to.

Question 33

Consider the marginal cost curve as a supply curve. What happens if price of an input happened to increase?

Answer 33

The supply curve is the same as the marginal cost curve. If the price of input increase, we would see that the marginal cost also increase. This would shift the entire supply curve. Since it has now become more expensive to produce, firms are less willing to produce the same output to the same price. Firms would now produce less at the same price. This means a left shift of the supply curve.

Question 34

What does the short run market supply curve tell us?

Answer 34

The short run market supply curve tells us what the entire industry (aggregated) will produce at every price level in the short run.

The market supply curve is of course equal to the sum of the individual ones. We add the quantity supplied at each price level to aggregate the market supply curve.

Question 35

Say we have a market supply curve (short run) that shows 0 quantity supplied for price levels beneath some threshold. What could this indicate?

Answer 35

It will most likely be an indication of the firm with the lowest average variable cost. This is because firms will shut down the business if price is smaller than the average variable cost. Therefore, nothing is supplied at this area.

Question 36

Why is it not easy to find the market supply curve?

Answer 36

You would think you could just add all the individual curves. In theory, you could. However, this is not possible in real life.

In real life, if price were to increase, ALL firms would increase production. This would cause an increased demand for the input variables. As a result, the price of inputs would increase as well. Therefore, the cost of production increase. Therefore, the supply curves will shift. The result is a highly unpredictable series of events.

Question 37

What is “price elasticity of market supply”?

Answer 37

Price elasticity of market supply measure the sensitivity of the entire industry’s output as a result of change in price. It is calcualted as always:

Es = (deltaQ/Q)/(deltaP/P) = (dQ/dP)*(P/Q)

The price elasticity of market supply shows the percentage change in quantity supplied by the entire industry as a result of a 1 percent change in price.

Question 38

What is perfectly inelastic supply?

Answer 38

Perfectly inelastic supply refers to the case where the entire industry’s plant and equipment is so fully utilized that it physically cannot handle more output. We would need to build new plant to produce more.

Question 39

What is perfectly elastic supply?

Answer 39

this happens when marginal cost is constant.

Question 40

What is producer surplus?

Answer 40

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

This is an area that can be calculated by an integral. Specifically, producer surplus is the area below price (horizontal due to perfect competition) and above the marginal cost curve.

If we first calculate the square using price and profit maximizing output level, then we can subtract the area under the marginal cost curve which gives us the producer surplus.

Question 41

What is “the other way” of defining producer surplus?

Answer 41

We can calculate producer surplus as the difference between the firm’s revenue and the firm’s total variable cost.

This is because adding all marginal costs will actually give us the total variable cost. Since we are interested in the difference between market price and marginal cost, we can generalize it to say: Difference between total revenue and total variable cost.

this basically says that producer surplus is the same as dekningsbidrag

Question 42

In the LONG run, what does the demand curve facing the firm look like?

Answer 42

We’re still considering competitive markets, therefore the firm will be a price taker. As a result, the demand curve facing the firm will be a horizontal line.

Question 43

How do we find the profit maximizing output level on the long run?

Answer 43

The same principle applies, marginal cost equals marginal revenue. The only difference between long run and short run is the fact that in the long run, more inputs are variable.

Question 44

For an equilibrium to arise in the long run, certain economic conditions must prevail. What are these conditions?

Answer 44

1) Firms must have no desire to enter or leave.

Question 45

Consider a case where a firm has bought equipment. What is the accounting profit for future business, and what is the economic profit?

Answer 45

The accountiung profit is the difference in revenues and cash flows. pi = R - wL

THe economic profit is:
pi = R - wL - rK

Question 46

What is zero-economic profit?

Answer 46

Zero economic profit means competitive returns. It means that we earn 0 when opportunity cost and etc is taken into account. Therefore, zero economic profit does not mean we are not making money, but it means we are not making more money than required for us to be in the industry. The firm is therefore performing adequately.

Question 47

Elaborate on entry and exit in regards to equilibrium in long run

Answer 47

If the industry is “profitable”, many entries will happen. This will increase supply, which will drive prices down, which will decrease profitability. Therefore, it will be a balancing procedure.

The same happens with the opposite scenario.

Question 48

A long run competitive equilibrium occurs when …

Answer 48

1) All firms are maximizing porifts

2) No firm has en incentive either to enter or exit the industry because all firms are earning zero economic profit

3) The price of the product is such that the quantity supplied by the industry is equal to the quantity demanded by consumers

Question 49

elaborate on expenditure and that shite

Answer 49

so, if we are a firm and are considering our costs: We look at individual input types. Say type i for I=1 to N. Then we look at the price we pay for input i and the quantity of input i. If we assume we get discount from buying larger quanta, we would be too “simple” if we consider a fixed price. Therefore, we say that the total expenditure for input I is: w_i(x_i) * x_i. w_i takes the quantity of input i as argument and gives the price we pay per unit/for the last unit when we buy x_i amount. We differ between average price and price when x_i amount because the price change dependent on the quantity. Anyways, the price acts like the average price.

If we consider the effect of buying another unit of the input, we need to take into account both the price of the next unit, and the change this extra unit has on the previous x_i - 1 units. Thus, marginal expenditure refers the effect of buying another unit.

if we sum together the total expenditure for all our units, we get total costs.

Question 50

How does expenditure relate to costs?

Answer 50

Costs are per output unit. Expenditure is per unit of input.

Marginal cost is the cost required to produce another unit.

Marginal expenditure is the effect on the input when we buy one more unit rather than some current number
.

Question 51

Why is marginal expenditure of input i given as: dw_i/dx_i * x_i + w_i

Answer 51

w_i is the price we pay for the x_i’th unit of input i. In a sense, this becomes the average price. However, we have to account for the effect that occurs on the previosuly considered units. This is the case if we follow a price function like w_i(x_i) = a - b(x_i)
When we buy 1 more unit, we buy this unit at a price that is lower than the price we would have payed for the previous units, and this price must be applied to the previous ones as well.

All of this sorty of assumes that we pay the same amount for all units. Therefore, when the price is reduced as a result of our firm buying another unit, we must reduce the price of the previous units as well. And this must of course be accounted for when we calculate marginal expenditure.

However, if we do not have any changes in price as we buy more, say perfect competition, than we can ignore all this, at just consider w_i as fixed.

Of course, this will only apply when we buy in bulk. If we buy in multiple sessions, we would not expect this kind of “reward” for bulk buying.

Question 52

How can we represent marginal revenue in terms of price elasticity of demand?

Answer 52

MR = dP/dq * q + P

MR = P(dP/dq * q/P + 1)

MR = P(1 - 1/(abs(Ep)))

Question 53

what is the most important result from profit maximization?

Answer 53

The most important result is that profit maximization implies cost minimization for some given output, revenue maximization for a given input, and an optimal trade off between every marginal revenue and marginal expenditure for every pair of outputs and inputs.