ec 311 - intermediate microeconomic theory - lecture: cost ... · ec 311 - intermediate...

EC 311 - Intermediate Microeconomic Theory

Lecture: Cost of Production

Bekah Selby

[email protected]

April 21, 2014

Selby EC 311 - Lectures April 21, 2014 1 / 26

Measuring Costs

What Costs Matter?

I What sorts of costs do firms face when making production decisions?

I Wages for employees

I Costs of materials and capital

I Rent for building space...

I Economic vs. Accounting Costs

I Accounting Cost: Actual expenses plus depreciation charges for capital

equipmentI Economic Cost: Cost to a firm of utilizing economic resources in

production

I Includes wages, rents, raw material costs, and something we call opportunity

costs


Measuring Costs

What Costs Matter?

I Opportunity Cost: Cost associated with opportunities forgone when a

firm’s resources are not put to their best alternative use.

I Example: A firm could choose to use the building that they own to

produce widgets. Their next best alternative use would be to rent out the

building to someone else. The opportunity cost of producing these widgets

includes this forgone rental income.

I Economic costs boil down to just opportunity costs....

I Wages are resources that the firm could have used to buy materials

I The building space could have been used to get rental income

Economic Cost = Opportunity Cost


Measuring Costs

What Costs Matter?

As economists, it is essential account for opportunity costs. However, there

are types of costs that we don’t consider important in the decisions making

process of firms.

I Sunk Costs: Expenditures that have been made and cannot be recovered

I Perhaps a county has a fee for a business to apply for building permits

I After the business pays the fee, there is no way for them to put that same

money to an alternative use.

I Thus the fee is considered a sunk cost of production and the opportunity

cost of the fee is zero.


Measuring Costs

What Costs Matter?

I Total Costs (TC): total economic costs of production. Has one part that

varies with output and another that does not

I Fixed Costs (FC): the cost of production that does not vary with the

amount of output produced.

I Examples: Lot rent, maintenance, heat/electricity, base number of

employees

I Variable Costs (VC): the cost of production that depends on the level of

output

I Examples: wages for employees, raw materials, etc.

TC = FC + VC


Measuring Costs

What Costs Matter?

I Fixed vs. Sunk Costs:

I Fixed costs can be avoided by shutting down/ going out of business

I The things that are fixed costs can then be put to other use (renting out lots

space, for example)

I Sunk costs, however, have been paid and cannot be recovered to used for

any other purpose.

I We must distinguish between the two because fixed costs affect the

decisions of the firm for future output where sunk costs do not.


Measuring Costs

What Costs Matter?

I Marginal Costs (MC) : increase in cost resulting in the production of

one extra unit of output

I Are marginal costs related to variable costs or fixed costs?

I They are related to variable costs...

MC =∆VC∆q

=∆TC∆q

I Why is marginal cost not related to fixed costs?


Measuring Costs

What Costs Matter?

I Average Total Cost (ATC): total cost divided by amount of output. It has

two parts: average fixed costs (AFC) and average variable costs (AVC)

ATC =TCq

=FC + VC

q=

FCq

+VCq

= AFC + AVC


Measuring Costs

What Costs Matter?

I Examples:

I Suppose that TC = 20 + 4qI What is the FC and VC of production?

I FC = 20

I VC(q) = 4q

I What is the MC?

I MC(q) = ∆VC∆q = 4

I What is the AFC, AVC, and ATC?

I AFC(q) = FCq = 20

q

I AVC = VCq = 4q

q = 4

I ATC(q) = AFC + AVC = 20q + 4


Measuring Costs

What Costs Matter?

Example: Complete the table:

q FC VC TC MC AFC AVC ATC

0 50 0 - - - -

1 50 50

2 50 78

3 50 98

4 50 112


Measuring Costs

What Costs Matter?

Example: Complete the table:

q FC VC TC MC AFC AVC ATC

0 50 0 50 - - - -

1 50 50 100 50 50 50 100

2 50 78 128 28 25 39 64

3 50 98 148 20 16.7 32.7 49.3

4 50 112 162 14 12.5 28 40.5


Short-Run

Costs in the Short-Run

I Recall that in the short-run, some factors of production are fixed

I Consider the case where labor is the only variable:

I For each unit of labor, L, the cost is w

I Then a change in the VC here is

∆VC = w∆L

I So MC is then

MC =∆VC∆q

=w∆L∆q

=w

∆q/∆L=

wMPL

I As the MPL goes up, what happens to MC?Selby EC 311 - Lectures April 21, 2014 12 / 26

Short-Run

The Shapes of Cost Curves

I As q goes up:

I TC increases

I VC increases

I FC doesn’t change

I For low levels of output MC/AVC/ATC decrease, but increase for higher

levels of q

I AFC decreases as q increases

I This is easier seen graphically


Short-Run


Short-Run


I AVC vs MC

I For low leves of output, AVC is larger than MC

I But as q increases, MC increases faster than AVC

I We can find the MC by taking the partial derivative of the VC curve.

MC =∂VC∂q

I So the point at which the MC curve and the AVC intersect is when

MC =∂VC∂q

=VCq

= AVC


Short-Run


I Examples:

TC = 40 + 8q2

q = k̄L

I What are the FC and VC?

I FC = 40

I VC = 8q2 = 8(k̄L)2

I What are MC?

I MC = ∂VC∂q = 16q = 16k̄L


Short-Run


I Examples:

TC = 40 + 8q2

q = k̄L

I What are the AFC and AVC?

I AFC = 40/q = 40/(k̄L)

I AVC = 8q2/q = 8q = 8(k̄L)


Long-Run

Cost in the Long-Run

I In the long-run, firms are subject to capital costs.

I User Cost of Capital: Annual cost of owning and using a capital asset,

equal to depreciation plus forgone interest(returns if invested elsewhere)

I Usually we illustrate the user cost as a “rental" rate:

r ≡ Depreciation Rate + Interest Rate = δ + i

I So if capital for a firm depreciates at a rate of 3% per year and it could

have earn 10% if invested elsewhere. What is the rental rate of capital?

I r = δ + i = 3% + 10% = 13%

I So the cost of capital is rK = 0.13KSelby EC 311 - Lectures April 21, 2014 18 / 26

Long-Run

The Isocost Line

I So the cost a firm faces in the long run is a combination of labor costs

and capital costs:

C = wL + rK

I Isocost Line: A graph shoing all possible combinations of L and K that

cost the firm the same amount

I What is the slope of the isocost line?

I Rewrite the isocost line as K =(C

r

)−(w

r

)L

I Then the slope is ∆K/∆L = −(w/r)


Long-Run

The Firm’s Decision

I From chapter 6, we saw that the firm had a production function

q = F(K,L)

I From this discussion, we know that the firm also faces a cost for

producing using inputs K and L

C = wL + rK


Long-Run


I So the firm’s problem is to choose the level of inputs to use to minimize

their total costs of producing some output level q∗

minK,L

C = wL + rK

s.t. F(K,L) = q∗


Long-Run



Long-Run

Input Substitution

I What happens when the price of labor increases?

I The isocost curve becomes steeper.

I So produce the same level of output, the firm will substitute capital for

labor:


Long-Run

Expansion Path and Long-Run Costs

I Quantity of output is not necessarily constant over time

I As quantity goes up, the cost minimizing bundle of (K,L) changes and

the total cost of production increases

I Thus the firm reoptimizes for each level of desired output.

I The curve connecting these bundes is called the firm’s expansion path


Long-Run


Long-Run

I At each level of q, the minimized cost of production is C(q) which is

increasing in q. This is the long-run total cost curve.


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