EC 311 - Intermediate Microeconomic Theory

Home , Economic cost

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 equipment

I 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...

∆VC ∆TC MC = = ∆q ∆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)

TC FC + VC FC VC ATC = = = + = AFC + AVC q q q q

Selby EC 311 - Lectures April 21, 2014 8 / 26 Measuring Costs

What Costs Matter?

I Examples:

I Suppose that TC = 20 + 4q

I What is the FC and VC of production?

I FC = 20

I VC(q) = 4q

I What is the MC?

∆VC I MC(q) = ∆q = 4

I What is the AFC, AVC, and ATC?

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

∆VC w∆L w w MC = = = = ∆q ∆q ∆q/∆L MPL

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.

∂VC MC = ∂q

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

∂VC VC MC = = = AVC ∂q q

Selby EC 311 - Lectures April 21, 2014 15 / 26 Short-Run

The Shapes of Cost Curves

I Examples: TC = 40 + 8q2

q = ¯kL

I What are the FC and VC?

I FC = 40

2 2 I VC = 8q = 8(¯kL)

I What are MC? ∂VC ¯ I MC = ∂q = 16q = 16kL

Selby EC 311 - Lectures April 21, 2014 16 / 26 Short-Run

The Shapes of Cost Curves

I Examples: TC = 40 + 8q2

q = ¯kL

I What are the AFC and AVC?

I AFC = 40/q = 40/(¯kL)

2 I AVC = 8q /q = 8q = 8(¯kL)

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 = 0.13K Selby 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?

C w I Rewrite the isocost line as K = r − 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∗

min C = wL + rK K,L

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