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EC 311 - Intermediate Microeconomic Theory
Lecture: Cost of Production
Bekah Selby
rebekahs@uoregon.edu
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
Selby EC 311 - Lectures April 21, 2014 2 / 26
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
Selby EC 311 - Lectures April 21, 2014 3 / 26
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.
Selby EC 311 - Lectures April 21, 2014 4 / 26
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
Selby EC 311 - Lectures April 21, 2014 5 / 26
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.
Selby EC 311 - Lectures April 21, 2014 6 / 26
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?
Selby EC 311 - Lectures April 21, 2014 7 / 26
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
Selby EC 311 - Lectures April 21, 2014 8 / 26
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
Selby EC 311 - Lectures April 21, 2014 9 / 26
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
Selby EC 311 - Lectures April 21, 2014 10 / 26
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
Selby EC 311 - Lectures April 21, 2014 11 / 26
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
Selby EC 311 - Lectures April 21, 2014 13 / 26
Short-Run
Selby EC 311 - Lectures April 21, 2014 14 / 26
Short-Run
The Shapes of Cost Curves
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
Selby EC 311 - Lectures April 21, 2014 15 / 26
Short-Run
The Shapes of Cost Curves
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
Selby EC 311 - Lectures April 21, 2014 16 / 26
Short-Run
The Shapes of Cost Curves
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)
Selby EC 311 - Lectures April 21, 2014 17 / 26
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)
Selby EC 311 - Lectures April 21, 2014 19 / 26
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
Selby EC 311 - Lectures April 21, 2014 20 / 26
Long-Run
The Firm’s Decision
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∗
Selby EC 311 - Lectures April 21, 2014 21 / 26
Long-Run
The Firm’s Decision
Selby EC 311 - Lectures April 21, 2014 22 / 26
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:
Selby EC 311 - Lectures April 21, 2014 23 / 26
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
Selby EC 311 - Lectures April 21, 2014 24 / 26
Long-Run
Selby EC 311 - Lectures April 21, 2014 25 / 26
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.
Selby EC 311 - Lectures April 21, 2014 26 / 26
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