Chapter 14: The Costs of Production

Fundamental Objectives and the Firm's Goal

• Primary Assumption of the Firm: The fundamental goal of a firm is to maximize its total profit.

• Total Revenue ($TR$): The total amount a firm receives for the sale of its output. It is calculated using the formula:     $TR = P \times Q$     Where $P$ is the price and $Q$ is the quantity of output.

• Total Cost ($TC$): The market value of all the inputs a firm uses in production.

• Profit: The difference between total revenue and total cost:     $\text{Profit} = TR - TC$

Example 1A: Jelani’s Gelato Shop (Basic Profit)

• Scenario Details:

  • Jelani produces $15,000$ pints of gelato annually.

  • Selling price: $\$5$ per pint.

  • Total annual costs: $\$65,000$.

• Calculations:

  • $TR = \$5 \times 15,000 = \$75,000$

  • $\text{Profit} = \$75,000 - \$65,000 = \$10,000$

The Significance of Opportunity Costs

• The Principle: Under the tenet that "the cost of something is what you give up to get it," economic costs must include all opportunity costs.

• Explicit Costs: Input costs that require a direct outlay of money by the firm.

  • Named Example: Paying wages to employees.

• Implicit Costs: Input costs that do not require an outlay of money by the firm.

  • Named Example: The opportunity cost of the owner’s time (what they could have earned elsewhere).

• Total Economic Cost: The sum of both categories:     $\text{Total Cost} = \text{Explicit Costs} + \text{Implicit Costs}$

Example 1B: Jelani’s Explicit and Implicit Costs

• Scenario Details:

  • Raw materials cost: $\$20,000$

  • Rent: $\$12,000$

  • Alternative employment opportunity: Working at a coffee shop for $\$25,000$ per year.

• Calculations:

  • Explicit Costs: $\$20,000 + \$12,000 = \$32,000$

  • Implicit Costs: $\$25,000$

  • Total Costs: $\$32,000 + \$25,000 = \$57,000$

Example 1C: The Cost of Capital for Jelani

• Scenario Details: Jelani invested $\$80,000$ to start the business. This was financed by:

  1. Withdrawing $\$30,000$ from savings.

  2. Borrowing $\$50,000$ from a bank.

  3. Interest rate for both saving and borrowing is $10\%$.

• Calculations:

  • Explicit Cost: Interest paid on the borrowed amount: $0.10 \times \$50,000 = \$5,000$

  • Implicit Cost: Forgone interest on the savings: $0.10 \times \$30,000 = \$3,000$

  • Total Opportunity Cost of Capital: $\$8,000$ per year.

Economic Profit vs. Accounting Profit

• Accounting Profit: Calculated as Total Revenue minus only Total Explicit Costs.     $\text{Accounting Profit} = TR - \text{Explicit Costs}$

• Economic Profit: Calculated as Total Revenue minus Total Costs (sum of explicit and implicit).     $\text{Economic Profit} = TR - (\text{Explicit Costs} + \text{Implicit Costs})$

• Relationship: Accounting profit is always greater than economic profit because it ignores implicit costs.

Example 1D: Comprehensive Profit Analysis for Jelani

• Total Revenue: $\$75,000$

• Explicit Costs: $\$20,000 \text{ (materials)} + \$12,000 \text{ (rent)} + \$5,000 \text{ (interest)} = \$37,000$

• Implicit Costs: $\$25,000 \text{ (alt. job)} + \$3,000 \text{ (forgone interest)} = \$28,000$

• Accounting Profit: $\$75,000 - \$37,000 = \$38,000$

• Economic Profit: $\$75,000 - (\$37,000 + \$28,000) = \$10,000$

  • Alternatively: $\text{Economic Profit} = \text{Accounting Profit} - \text{Implicit Costs} = \$38,000 - \$28,000 = \$10,000$

The Production Function and Marginal Product

• Production Assumptions: In the short run, at least one resource is fixed (e.g., factory size). To increase output, a firm must hire more workers.

• Production Function: The relationship between the quantity of inputs (e.g., workers) and the quantity of output (e.g., goods produced).

  • The production function typically gets flatter as the quantity of input increases.

• Marginal Product: The increase in output resulting from one additional unit of input, holding other inputs constant.

• Marginal Product of Labor ($MPL$):     $MPL = \frac{\Delta Q}{\Delta L}$     Where $\Delta Q$ is the change in output and $\Delta L$ is the change in labor.

Example 2A & 2B: Xavier’s Popcorn Truck Production

• Fixed Resource: A popcorn truck.

• Variable Input: Workers ($L$).

• Data Table:

  • $L = 0$, $Q = 0$; $MPL = -$

  • $L = 1$, $Q = 30$; $MPL = 30$

  • $L = 2$, $Q = 55$; $MPL = 25$

  • $L = 3$, $Q = 75$; $MPL = 20$

  • $L = 4$, $Q = 90$; $MPL = 15$

  • $L = 5$, $Q = 100$; $MPL = 10$

Diminishing Marginal Product

• Definition: The property whereby the marginal product of an input declines as the quantity of the input increases.

• Graphical Representation: The slope of the production function decreases (the curve flattens).

• Marginal Thinking: "Rational people think at the margin." Hiring an extra worker increases output by the $MPL$ but increases costs by the wage paid.

Measures of Cost

• Total Cost ($TC$): The sum of Fixed and Variable costs.     $TC = FC + VC$

• Fixed Costs ($FC$): Costs that do not vary with the quantity of output produced. These are incurred even if production is zero (e.g., rent, equipment cost).

• Variable Costs ($VC$): Costs that vary directly with the quantity of output produced (e.g., raw materials, wages).

Example 3: Angel’s Knitted Scarves Business

• Data Set:

  • Fixed Cost ($FC$): $\$18$ (cost of two pairs of knitting needles).

  • $Q=0$: $VC=0$, $TC=18$

  • $Q=1$: $VC=15$, $TC=33$

  • $Q=2$: $VC=25$, $TC=43$

  • $Q=3$: $VC=30$, $TC=48$

  • $Q=4$: $VC=32$, $TC=50$

  • $Q=5$: $VC=36$, $TC=54$

  • $Q=6$: $VC=44$, $TC=62$

  • $Q=7$: $VC=58$, $TC=76$

  • $Q=8$: $VC=78$, $TC=96$

  • $Q=9$: $VC=104$, $TC=122$

  • $Q=10$: $VC=136$, $TC=154$

Average and Marginal Costs

• Average Fixed Cost ($AFC$): Fixed cost divided by the quantity of output.     $AFC = \frac{FC}{Q}$

  • $AFC$ always declines as $Q$ rises.

• Average Variable Cost ($AVC$): Variable cost divided by the quantity of output.     $AVC = \frac{VC}{Q}$

• Average Total Cost ($ATC$): Total cost divided by the quantity of output.     $ATC = \frac{TC}{Q} = AFC + AVC$

  • Describes the cost of a typical unit produced.

• Marginal Cost ($MC$): The increase in total cost resulting from an additional unit of production.     $MC = \frac{\Delta TC}{\Delta Q}$

Relationships Between Cost Curves

• The Efficient Scale: The quantity of output that minimizes Average Total Cost.

• MC and ATC Relationship:

  • When MC < ATC, Average Total Cost is falling.

  • When MC > ATC, Average Total Cost is rising.

  • The $MC$ curve crosses the $ATC$ curve at its minimum point.

• Graphical Shapes:

  • $TC$ and $VC$ curves are parallel lines (separated by the constant amount of $FC$).

  • $FC$ is a horizontal line.

  • $MC$ typically rises with production.

  • $ATC$ is typically U-shaped.

Costs in the Short Run vs. the Long Run

• Short Run (SR): A period in which some inputs are fixed (e.g., the size of the factory). The costs associated with fixed inputs are Fixed Costs.

• Long Run (LR): A period in which all inputs are variable. Firms can build new factories, sell existing ones, or change any input.

• Long-Run Average Total Cost ($LRATC$): The path along the lowest points of the various Short-Run Average Total Cost ($SRATC$) curves corresponding to different factory sizes (e.g., small, medium, large).

  • The $LRATC$ at any $Q$ is the cost per unit using the most efficient mix of inputs for that quantity.

Returns to Scale

• Economies of Scale: $LRATC$ falls as the quantity of output increases.

  • Cause: Often due to increasing specialization among workers.

  • Usually occurs at low levels of output.

• Constant Returns to Scale: $LRATC$ stays the same as the quantity of output changes.

• Diseconomies of Scale: $LRATC$ rises as the quantity of output increases.

  • Cause: Coordination problems inherent in large organizations (e.g., management becomes stretched, communication breaks down).

  • Usually occurs at high levels of output.

Questions & Discussion

Active Learning 1: Favorite Frozen Yogurt Shop

• Prompt: List three costs and three business decisions affected by them.

• Discussion Context: This exercise encourages students to identify fixed vs. variable costs and marginal decisions like hiring or pricing.

Active Learning 2: Economic vs. Accounting Profit

• Scenario: Equilibrium rent on office space increases by $\$500/\text{month}$.

• A. If you rent the office space:

  • Explicit costs increase by $\$500$.

  • Both accounting and economic profit fall by $\$500/\text{month}$.

• B. If you own the office space:

  • Explicit costs remain unchanged; accounting profit does not change.

  • Implicit costs (opportunity cost of the space) increase by $\$500$.

  • Economic profit falls by $\$500/\text{month}$.

Active Learning 3: Diminishing MPL Calculation

• Workers: 0, 1, 2, 3, 4, 5

• Output: 0, 45, 85, 115, 135, 145

• MPL Values: 45, 40, 30, 20, 10

• Answers:

  • $MPL$ of second worker: $40$

  • $MPL$ of fourth worker: $20$

  • Does it exhibit diminishing marginal returns? Yes.

Active Learning 4: Calculating Costs Table

• Data provided:

  • $Q=0$, $TC=\$50$ ($FC=\$50$)

  • $Q=1$, $MC=10$, $TC=60$, $VC=10$, $AFC=50$, $AVC=10$, $ATC=60$

  • $Q=2$, $TC=80$, $VC=30$, $AFC=25$, $AVC=15$, $ATC=40$, $MC=20$

  • $Q=3$, $VC=60$, $TC=110$, $AFC=16.67$, $AVC=20$, $ATC=36.67$, $MC=30$

  • $Q=4$, $ATC=37.50$, $TC=150$, $VC=100$, $AFC=12.50$, $AVC=25$, $MC=40$

  • $Q=5$, $VC=150$, $TC=200$, $AFC=10$, $AVC=30$, $ATC=40$, $MC=50$

  • $Q=6$, $TC=260$, $VC=210$, $AFC=8.33$, $AVC=35$, $ATC=43.33$, $MC=60$