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2.4 — Costs of Production

ECON 306 • Microeconomic Analysis • Fall 2021

Ryan Safner
Assistant Professor of Economics
safner@hood.edu
ryansafner/microF21
microF21.classes.ryansafner.com

Outline

Opportunity Costs in Production

Costs in the Short Run

Costs in the Long Run

Recall: The Firm's Two Problems

1st Stage: firm's profit maximization problem:

  1. Choose: < output >

  2. In order to maximize: < profits >

2nd Stage: firm's cost minimization problem:

  1. Choose: < inputs >

  2. In order to minimize: < cost >

  3. Subject to: < producing the optimal output >

  • Minimizing costs ⟺ maximizing profits

A Competitive Market

  • We assume (for now) the firm is in a competitive industry:

  1. Firms’ products are perfect substitutes

  2. Firms are “price-takers”, no one firm can affect the market price

  3. Market entry and exit are free†

† Remember this feature. It turns out to be the most important feature that distinguishes different types of industries!

Profit

  • Recall that profit is: π=pq⏟revenues−(wl+rk)⏟costs

  • We’ll first take a closer look at costs today

  • Next class we’ll put costs together with revenues to find optimal q∗ that maximizes π (the first stage problem)

Opportunity Costs in Production

Production Costs are Opportunity Costs

  • Remember, economic costs are broader thanthe common conception of “cost”
    • Accounting cost: monetary cost
    • Economic cost: value of next best alternative use of resources given up (i.e. opportunity cost)

Production Costs are Opportunity Costs

  • This leads to the difference between

    • Accounting profit: revenues minus accounting costs
    • Economic profit: revenues minus accounting & opportunity costs

  • A really difficult concept to think about!

Production Costs are Opportunity Costs

  • Another helpful perspective:

  • Accounting cost: what you historically paid for a resource

  • Economic cost: what you can currently get in the market for a selling a resource

    • Resource's value in alternative uses

A Reminder: It's Demand all the Way Down!

  • Supply is actually Demand in disguise!

  • The (opportunity) cost producers must pay to purchase (scarce) inputs to produce products comes from the fact that other people demand those same inputs to consume or produce other things for other purposes!

    • You are not paying the price just to buy them, but also to pull them out of other valuable lines of production in the economy!

Production Costs are Opportunity Costs

  • Because resources are scarce, and have rivalrous uses, how do we know we are using resources efficiently??

  • In functioning markets, the market price measures the opportunity cost of using a resource for an alternative use

  • Firms not only pay for direct use of a resource, but also indirectly compensate society for "pulling the resource out" of alternate uses in the economy!

Production Costs are Opportunity Costs

  • Every choice incurs an opportunity cost

Examples:

  • If you start a business, you may give up your salary at your current job
  • If you invest in a factory, you give up other investment opportunities
  • If you use an office building you own, you cannot rent it to other people
  • If you hire a skilled worker, you must pay them a high enough salary to deter them from working for other firms

Opportunity Cost is Hard for People

Opportunity Costs vs. Sunk Costs

  • Opportunity cost is a forward-looking concept

  • Choices made in the past with non-recoverable costs are called sunk costs

  • Sunk costs should not enter into future decisions

  • Many people have difficulty letting go of unchangeable past decisions: sunk cost fallacy

Sunk Costs: Examples

Sunk Costs: Examples

Sunks Costs: Examples

Common Sunk Costs in Business

  • Licensing fees, long-term lease contracts

  • Specific capital (with no alternative use): uniforms, menus, signs

  • Research & Development spending

  • Advertising spending

The Accounting vs. Economic Point of View I

  • Helpful to consider two points of view:

  1. “Accounting point of view”: are you taking in more cash than you are spending?

  2. “Economic point of view”: is your product you making the best social use of your resources

    • i.e. are there higher-valued uses of your resources you are keeping them out of?

The Accounting vs. Economic Point of View II

  • Implications for society: are consumers best off with you using scarce resources (with alternative uses!) to produce your current product?

  • Remember: this is an economics course, not a business course!

    • Economists are pro-market, not pro-business!
    • What might be good/bad for one business might have bad/good consequences for society!

Costs in the Short Run

Costs in the Short Run

  • Total cost function, C(q) relates output q to the total cost of production C

C(q)=f+VC(q)

Costs in the Short Run

  • Total cost function, C(q) relates output q to the total cost of production C

C(q)=f+VC(q)

  • Two kinds of short run costs:

1. Fixed costs, f are costs that do not vary with output

  • Only true in the short run! (Consider this the cost of maintaining your capital)

Costs in the Short Run

  • Total cost function, C(q) relates output q to the total cost of production C

C(q)=f+VC(q)

  • Two kinds of short run costs:

1. Fixed costs, f are costs that do not vary with output

  • Only true in the short run! (Consider this the cost of maintaining your capital)

2. Variable costs, VC(q) are costs that vary with output (notice the variable in them!)

  • Typically, the more production of q, the higher the cost
  • e.g. firm is hiring additional labor

Fixed vs. Variable costs: Examples

Example: Airlines

Fixed costs: the aircraft

Variable costs: getting one more customer in a seat

Fixed vs. Variable costs: Examples

Example: Car Factory

Fixed costs: the factory, machines in the factory

Variable costs: producing one more car

Fixed vs. Variable costs: Examples

Example: Starbucks

Fixed costs: the retail space

Variable costs: selling one more cup of coffee

Fixed vs. Sunk costs

  • Diff. between fixed vs. sunk costs?

  • Sunk costs are a type of fixed cost that are not avoidable or recoverable

  • Many fixed costs can be avoided or changed in the long run

  • Common fixed, but not sunk, costs:

    • rent for office space, durable equipment, operating permits (that are renewed)

  • When deciding to stay in business, fixed costs matter, sunk costs do not!

Cost Functions: Example

Example: Suppose your firm has the following total cost function:

C(q)=q2+q+10

  1. Write a function for the fixed costs, f.

  2. Write a function for the variable costs, VC(q).

Cost Functions: Example, Visualized

q f VC(q) C(q)
0 10 0 10
1 10 2 12
2 10 6 16
3 10 12 22
4 10 20 30
5 10 30 40
6 10 42 52
7 10 56 66
8 10 72 82
9 10 90 100
10 10 110 120

Average Costs

  • Average Fixed Cost: fixed cost per unit of output:

AFC(q)=fq

Average Costs

  • Average Fixed Cost: fixed cost per unit of output:

AFC(q)=fq

  • Average Variable Cost: variable cost per unit of output:

AVC(q)=VC(q)q

Average Costs

  • Average Fixed Cost: fixed cost per unit of output:

AFC(q)=fq

  • Average Variable Cost: variable cost per unit of output:

AVC(q)=VC(q)q

  • Average (Total) Cost: (total) cost per unit of output:

AC(q)=C(q)q

Marginal Cost

  • Marginal Cost is the change in total cost for each additional unit of output produced:

MC(q)=ΔC(q)Δq≈C2−C1q2−q1

  • Calculus: first derivative of the cost function

  • Marginal cost is the primary cost that matters in making decisions

    • All other costs are driven by marginal costs
    • This is the main cost that firms can “see”

The Importance of Marginal Cost

Dazexiang Rebellion against the Qin Dynasty (209 B.C.)

Average and Marginal Costs: Example

Example: A small farm grows strawberries on 5 acres of land that it rents for $200 a week. The farm can hire workers at a wage of $250/week for each worker. The table below shows how the output of strawberries (in truckloads) varies with the number of workers hired:

Output Labor
0 0
1 1
2 3
3 7
4 12
5 18
  1. If labor is the only variable cost, calculate the MC(q) and AC(q) for each of the first 5 truckloads.

Average and Marginal Costs: Visualized

q C(q) MC(q) AFC(q) AVC(q) AC(q)
0 10 − − − −
1 12 2 10.00 2 12.00
2 16 4 5.00 3 8.00
3 22 6 3.33 4 7.30
4 30 8 2.50 5 7.50
5 40 10 2.00 6 8.00
6 52 12 1.67 7 8.70
7 66 14 1.43 8 9.40
8 82 16 1.25 9 10.25
9 100 18 1.11 10 11.10
10 120 20 1.00 11 12.00

Relationship Between Marginal and Average

  • Mathematical relationship between a marginal & an average value

  • If marginal < average, then average ↓

Relationship Between Marginal and Average

  • Mathematical relationship between a marginal & an average value

  • If marginal < average, then average ↓

  • If marginal > average, then average ↑

Relationship Between Marginal and Average

  • Mathematical relationship between a marginal & an average value

  • If marginal < average, then average ↓

  • If marginal > average, then average ↑

  • When marginal = average, average is maximized/minimized

  • When MC=AC, AC is at a minimum

  • When MC=AVC, AVC is at a minimum

  • Economic importance (later): Break-even price & shut-down price

Short Run Costs: Example

Example: Suppose a firm's cost structure is described by: C(q)=15q2+8q+45MC(q)=30q+8

  1. Write expressions for the firm's fixed costs, variable costs, average fixed costs, average variable costs, and average (total) costs.

  2. Find the minimum average (total) cost.

  3. Find the minimum average variable cost.

Costs: Example: Visualized

Costs in the Long Run

Costs in the Long Run

  • Long run: firm can change all factors of production & vary scale of production

  • Long run average cost, LRAC(q): cost per unit of output when the firm can change both l and k to make more q

  • Long run marginal cost, LRMC(q): change in long run total cost as the firm produce an additional unit of q (by changing both l and/or k)

Average Cost in the Long Run

  • Long run: firm can choose k (factories, locations, etc)

  • Separate short run average cost (SRAC) curves for each amount of k potentially chosen

Average Cost in the Long Run

  • Long run: firm can choose k (factories, locations, etc)

  • Separate short run average cost (SRAC) curves for each amount of k potentially chosen

  • Long run average cost (LRAC) curve "envelopes" the lowest (optimal) parts of all the SRAC curves!

"Subject to producing the optimal amount of output, choose l and k to minimize cost"

Long Run Costs & Scale Economies I

  • Further important properties about costs based on scale economies of production: change in average costs when output is increased (scaled)

  • Economies of scale: average costs fall with more output

    • High fixed costs AFC>AVC(q) low variable costs

  • Diseconomies of scale: average costs rise with more output

    • Low fixed costs AFC<AVC(q) high variable costs

  • Constant economies of scale: average costs don’t change with more output

    • Firm at minimum average cost (optimal plant size), called minimum efficient scale (MES)

Long Run Costs & Scale Economies I

  • Note economies of scale ≠ returns to scale!

  • Returns to Scale (last class): a technological relationship between inputs & output

  • Economies of Scale (this class): an economic relationship between output and average costs

Long Run Costs & Scale Economies II

  • Minimum Efficient Scale: q with the lowest AC(q)

  • Economies of Scale: ↑q, ↓AC(q)

  • Diseconomies of Scale: ↑q, ↑AC(q)

Long Run Costs and Scale Economies: Example

Example: A firm's long run cost structure is as follows:

LRC(q)=32000q−250q2+q3LRMC(q)=32000−500q+3q2

  1. At what levels of output will the firm face economies of scale and diseconomies of scale? (Hint: This firm has a U-shaped LRAC.)

Long Run Costs and Scale Economies: Example

Outline

Opportunity Costs in Production

Costs in the Short Run

Costs in the Long Run

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