12 and 13: Costs and Perfect Competition

Question 1

Which are two parts of costs economists consider?

Answer 1

Monetary price and the opportunity costs

Question 2

What is affectual forecasting?

Answer 2

Anticipating how they will feel in the future (knowing if something will bring you more joy than the alternative)

Question 3

What is Narrative fallacy?

Answer 3

Describes how flawed stories of the past influence one’s perception of the present and future.

Question 4

What are imputed costs/interest? (but also calculatory entrepreneur’s salary)

Answer 4

Opportunity costs

Question 5

How is Management accountig different from financial reporting?

Answer 5

The primary purpose of financial reporting is to communicate a company’s financial situation to the outside world. These statements are subject to legal constraints and regulations that are sometimes incompatible with the idea of opportunity costs.

Management accounting considers imputed costs.

Question 6

What does the production function illustrate?

Answer 6

It illustrates the maxinal output that can be produced if we use a particular amount of inputs (usually capital and labor).

It measures the relationship between the inputs (factors of production) and the output.

Question 7

Is the production function exogenous or endogenous?

Answer 7

exogenous

Question 8

Are the amounts of inputs and the output exogenous or endogenous?

Answer 8

Endogenous

Question 9

What is the marginal product?

Answer 9

The marginal product of a factor of production shows us by how much our production (output) increases if we use another unit of this factor of production

Question 10

How do we compute the marginal product?

Answer 10

We can compute the marginal product of a factor of production by computing the first derivative with respect to the factor of production:
Remember that the derivative tells you how two variables interact.

Thus, deriving x with respect to l tells you what the effect of a (very small) increase of the labor input on the output x is - and that is exactly the definition of marginal product.

Question 11

On what does the marginal product depend on?

Answer 11

For most production functions, the marginal product depends on the amount of inputs we already use.

Question 12

How do you derive the cost function from the production function?

Answer 12

1. Find the cost-minimizing quantities of every input for each output level x (for example Wage per unit)
2. Multiply these input quantities with their exogenous prices.

Question 13

How are average costs defined?

Answer 13

Average costs are equal to the total costs divided by the total amount produced.

Question 14

How are fixed costs defined?

Answer 14

Fixed costs are independent of the quantity that is produced.

Question 15

What are the two types of Fixed costs? Which one do we consider?

Answer 15

Technological Fixed costs and contractual fixed costs

Technological fixed costs can be avoided if the production is completely stopped (x = 0), while contractual fixed costs have to be paid even if nothing is produced at all.

For our production function, the fixed costs are contractual fixed costs

Question 16

What are Variable Costs

Answer 16

Variable costs is the part of the costs that depends on the amount that is produced.

Question 17

Average fixed costs

Answer 17

The average fixed costs are the fixed costs divided by the total quantity x that is produced.

Question 18

Average variable costs

Answer 18

The average variable costs are the variable costs divided by the total quantity x that is produced.

Question 19

What are Marginal costs?

Answer 19

The marginal costs show how a (very small) increase in the output x affects our costs C.
If we want to know how C is affected by x, we just take the derivative of C with respect to x.

Question 20

How are the Cost function and the Marginal cost related to eachother?

Answer 20

The marginal cost function is the derivative of the cost function.

Question 21

How are the Cost function and the average cost function related?

Answer 21

The average cost function is the cost function over x.

Question 22

Where does the marginal cost function and the average cost function intersect?

Answer 22

The marginal costs intersect the average costs at their minimum.

Question 23

How are the fixed Costs depicted in a graph?

Answer 23

The fixed costs are FC = 1 (horizontal line) and independent of x.

Question 24

How does the average fixed cost function behave when the production quantity increases?

Answer 24

The average fixed costs AFC(x) = 1/x are decreasing with the production quantity x. (downward slope)

Question 25

How does the average variable costs function look like as a graph?

Answer 25

The average variable costs are AVC(x) = x

Straigh line, bisect the upper right quadrant

Question 26

How does the variable costs function look?

Answer 26

The variable costs are VC (x) = x^2

Upward slope

Question 27

What does the concept of “returns to scale” answer?

Answer 27

How an increase of the output x affects average costs.

They simulate a proportional increase of all inputs (for instance, we could double the amount of capital and labor) and check what happens to the output.

Question 28

What does constant return to scale or increasing/decreasing returns to scale mean?

Answer 28

If the output increases exactly proportionally (exactly doubles), we say the production function has constant returns to scale.

If the output increases more (less) than proportionally, the production function has increasing/decreasing returns to scale.

Question 29

Definition Returns to scale

Answer 29

Returns to scale measure the effect of a simultaneous, proportional increase of all factors of production on the output and the average costs.

A production function has increasing (constant, decreasing) returns to scale if the average costs are decreasing (constant, increasing).

Question 30

What do we use these different cost fubctions for?

Answer 30

We can use our cost functions to determine which amount x our firm should actually produce. In particular, our firm must decide which output x maximizes its profits for a given market price p.

Question 31

Which assumption do we make in a perfect market (firms operate under perfect competition)?

Answer 31

Assumption: firms take prices as given

Firms are price-takers - that is, each firm is so small compared to the whole market, that they have basically no effect on the market price.
Thus, they take the market price p as exogenously given.

Question 32

How does the profit function look like?

Answer 32

Revenue (quantity sold x times price per unit p) minus the costs of producing the amount x, C(x).

Thus:
px-C(x)

Question 33

First-order condition: What does this condition show us?

Answer 33

We obtain a condition that shows us which quantity x maximizes the profits M by taking the derivative of M with respect to x.

If we set this derivative equal to 0, we obtain the first order condition.

Question 34

What is the derivative of the profit function?

Answer 34

Market price p minus Marginal costs.

Question 35

Why is the derivative of the profit function p-C(x)/x?

Answer 35

Because the derivative of the Cost function is the marginal cost function (C(x)/x)

Question 36

Which conclusion does the first order condition in the end show us?

Answer 36

MC(x) = p

The first order condition shows that the profit is maximized if the firm chooses a quantity x such that the marginal costs (MC (x)) are EQUAL to the market price p.

Question 37

Why does it make sense that the marginal costs have to be equal to the market price as a first condition?

Answer 37

The marginal costs tell us how much the production of the next unit increases our costs.

The market price tells us by how much the next unit increases our revenue.

Thus, if the marginal costs would be lower than the price, producing another unit would increase our profit, the costs would increase by less than the revenue! (The potential is not reached!)

In contrast, if the marginal costs would be higher than the market price, we should reduce our production x.

Only if the price is equal to the marginal costs, our profit is maximized!

Question 38

Why does the first condition not suffice?

Answer 38

Because we don’t know if first derivative = 0 (gradient =0) is a maximum or a minimum! And we need a maximum!

Question 39

Second-order condition: What do we have to do to know if it is a maximum or a minimum?

Answer 39

To be sure that the x we find with the first-order condition is actually a maximum and not a minimum, we must differentiate the first-order condition itself again with respect to x and obtain the second-order condition.

Question 40

How do we know if we found the maximum?

Answer 40

If the second derivative is bigger than 0.

Question 41

What do we have to do when we want to decide if it were better for a firm to leave the market and not produce?

Answer 41

We first decide whether a firm with contractual fixed costs (fixed costs that can not be avoided) should stop producing.

We compare the profit of the firm for x = 0 (no quantity produced) to the profit for the optimal, strictly positive amount according to the first-order condition.

Question 42

What does the short-run supply tell us?

Answer 42

If p<AVC (x), it would be better if the firm would stop produce and leave the market.

The price must at least cover the averave variable costs.

Question 43

Why is it called the “Short-run supply”?

Answer 43

A lot of economists argue that our discussion of contractual fixed costs is equivalent to the short-run supply decision:
As some fixed costs (contractual fixed costs!) cannot be avoided i the short run, they are treated as sunk costs and not relevant for the decision.

Question 44

What are sunk costs?

Answer 44

Sunk costs are costs that have already been incurred at a given point in time and thus, cannot be recovered.

Example:
You already bought a machine you cannot recover the costs (sell the machine) because for example this machine was produced according to your liking.

Question 45

What’s the difference between short-run supply vs. long-run supply?

Answer 45

In the long-run, also contractual fixed costs can be avoided by, for instance, cancelling all contracts and selling the firm.

Thus, in the long-run, contractual costs are also part of the decision of our manager.

Question 46

When does the firm produce in the long-run?

Answer 46

Our firm produces a positive amount only if the profit is not negative.

This is the case if p is bigger or equal to the average costs.

This means the market price covers all the costs of production, including the contractual fixed costs.

Question 47

Firms make no profits in the long-run in perfectly competitve markets?

Answer 47

In the long run, the competitive forces in the market lead to a situation where firms only earn a “normal profit” (zero economic profit). This is the result of free entry and exit, which drives the price to the point where it equals the minimum average total cost. Hence, in perfectly competitive markets, firms earn no profit in the long run because competition eliminates any opportunities for sustained above-normal profits.

Question 48

What does “no profit” mean in this sense?

Answer 48

No profit means that these firms do not make any profits from an economist’s point of view.

Remember that economists also consider opportunity costs as part of the costs of production, while opportunity costs (e.g. potential of wages of self-employed owners) are not reporten on an actual balance sheet of firms in the real world.