Micro Exam 2

Fundamentals of Producer Theory and Opportunity Cost

• Producer Theory Overview:     * Consumer theory focuses on the study of demand curves.     * Producer theory focuses on the study of firm decisions which lead to supply curves.     * The primary goal of a firm is to maximize profit.

• Defining Profit and Revenue:     * Profit: Defined as Total Revenue minus Total Cost.         * $\text{Profit} = \text{Total Revenue} - \text{Total Cost}$     * Total Revenue (TR): The amount a firm receives for the sale of its output.         * $TR = P \times Q$         * $P = \text{Price}$         * $Q = \text{Quantity}$     * Total Cost: The market value of the inputs a firm uses in production.

• Opportunity Cost and Input Costs:     * Opportunity Cost: All those things forgone to acquire an item; specifically, the cost required to obtain those things.     * Explicit Costs: Input costs that require a direct monetary outlay by the firm. These are instances where money is physically exchanged. Accountants specifically include these costs.     * Implicit Costs: Input costs that do NOT require a direct monetary outlay by the firm. Economists include these in their calculations.         * Forgone Interest: This is the cost of capital as an opportunity cost. For example, interest missed out on that money would have earned if left in a bank.

• Example: Coffee Shop Ownership:     * Explicit Cost Examples:         * Rent or lease payments for the building.         * Costs paid to suppliers for raw materials (coffee beans, water, creamer, etc.).         * Wages paid to workers.     * Implicit Cost Examples:         * Forgone Income: You could earn $\$50/\text{hour}$ as a web designer, but you choose to run the shop instead.         * Forgone Interest: Suppose you use $\$20,000$ in personal savings to start the shop. If you could have earned $3\%$ interest on those savings, you gave up $\$600$ in interest (\20,000 \times 0.03 = \$600$).

• Comparison of Profit Types:     * Accounting Profit: $\text{Accounting Profit} = \text{TR} - \text{Explicit Costs}$     * Accountants ignore implicit costs like lost interest.     * Economic Profit: $\text{Economic Profit} = \text{TR} - \text{Explicit Costs} - \text{Implicit Costs}$     * Economic profit is used for decision-making in the long run.     * Rule of Thumb: $\text{Accounting Profit} \geq \text{Economic Profit}$

The Production Function and Marginal Product

• Production Function (PF): The relationship between the quantity of inputs used to make a good and the quantity of output of that good. It represents the maximum output produced for a given level of inputs.

• Marginal Product (MP): The increase in output that arises from an additional unit of input.     * General Formula: $MP_{\text{input}} = \frac{\Delta Q}{\Delta \text{input}}$     * Marginal Product of Labor (MPL): $MP_L = \frac{\Delta Q}{\Delta L}$     * Rational people think at the margin when making production decisions.

• Data Example: Dog-Walking Firm (Production Function):     * Input (Labor, L) | Output (Dogs walked, Q) | Marginal Product of Labor (MPL)     * $0$ | $0$ | $-$     * $1$ | $30$ | $30$     * $2$ | $50$ | $20$     * $3$ | $66$ | $16$     * $4$ | $80$ | $14$     * $5$ | $92$ | $12$

• Diminishing Marginal Product:     * Holding all else constant, the marginal product of an input declines as the quantity of the input increases.     * In the dog-walking example, the $MP_L$ drops from $30$ to $20$, then to $16$, etc.     * Graphical Representation:         * The Production Function is concave (increasing at a decreasing rate) because of diminishing MP. The slope of the PF gets flatter as input increases.         * The Total Cost curve is convex (increasing at an increasing rate) as a direct inverse result.     * Intuition for Diminishing MP: Workers may distract each other, arrive late to appointments, or face scheduling challenges. A common constraint is the limitation of other fixed inputs.

Measures of Cost

• Fixed Cost (FC): Costs that do not vary with the quantity of output produced.     * Examples: Rent, salaried employees (paid a fixed amount regardless of performance).

• Variable Cost (VC): Costs that vary with the quantity of output produced.     * Examples: Raw materials, hourly wages (hours increased to produce more, cut back to produce less).

• Total Cost (TC): The sum of fixed and variable costs.     * $TC = FC + VC$

• Marginal Cost (MC): The increase in total cost that arises from producing an extra (additional) unit of output. It is the slope of the Total Cost curve.     * $MC = \frac{\Delta TC}{\Delta Q}$

• Average Measures:     * Average Total Cost (ATC): $\text{Total Cost} / \text{Quantity}$         * $ATC = \frac{TC}{Q} = \frac{FC + VC}{Q} = \frac{FC}{Q} + \frac{VC}{Q}$         * $ATC = AFC + AVC$     * Average Fixed Cost (AFC): $\text{Fixed Cost} / \text{Quantity}$         * $AFC = \frac{FC}{Q}$     * Average Variable Cost (AVC): $\text{Variable Cost} / \text{Quantity}$         * $AVC = \frac{VC}{Q}$

Cost Calculation Practice

• Example 1: Dog-Walking Firm (Direct Costs)     * Assumptions: Fixed cost for phone service = $\$50$. Variable cost per worker = $\$100$ per week.     * L | Q | MPL | FC | VC | TC     * $0$ | $0$ | $-$ | $\$50$ | $\$0$ | $\$50$     * $1$ | $30$ | $30$ | $\$50$ | $\$100$ | $\$150$     * $2$ | $50$ | $20$ | $\$50$ | $\$200$ | $\$250$     * $3$ | $66$ | $16$ | $\$50$ | $\$300$ | $\$350$     * $4$ | $80$ | $14$ | $\$50$ | $\$400$ | $\$450$     * $5$ | $92$ | $12$ | $\$50$ | $\$500$ | $\$550$

• Example 2: Comprehensive Cost Table Calculation     * Q | FC | VC | TC | MC | AFC | AVC | ATC     * $0$ | $100$ | $0$ | $100$ | $-$ | $-$ | $-$ | $-$     * $1$ | $100$ | $50$ | $150$ | $50$ | $100$ | $50$ | $150$     * $2$ | $100$ | $90$ | $190$ | $40$ | $50$ | $45$ | $95$     * $3$ | $100$ | $140$ | $240$ | $50$ | $33.3$ | $46.67$ | $80$     * $4$ | $100$ | $200$ | $300$ | $60$ | $25$ | $50$ | $75$     * $5$ | $100$ | $280$ | $380$ | $80$ | $20$ | $56$ | $76$     * $6$ | $100$ | $380$ | $480$ | $100$ | $16.67$ | $63.33$ | $80$

• Example 3: "Harder Example" Table     * Q | FC | VC | TC | MC | AFC | AVC | ATC     * $0$ | $24$ | $0$ | $24$ | $-$ | $-$ | $-$ | $-$     * $1$ | $24$ | $16$ | $40$ | $16$ | $24$ | $16$ | $40$     * $2$ | $24$ | $50$ | $74$ | $34$ | $12$ | $25$ | $37$     * $3$ | $24$ | $84$ | $108$ | $34$ | $8$ | $28$ | $36$     * $4$ | $24$ | $136$ | $160$ | $52$ | $6$ | $34$ | $40$     * $5$ | $24$ | $196$ | $220$ | $60$ | $4.8$ | $39.2$ | $44$     * $6$ | $24$ | $258$ | $282$ | $62$ | $4$ | $43$ | $47$

• Example 4: Combined Data Table     * L | Q | MP | FC | VC | TC | MC | AFC | AVC | ATC     * $0$ | $0$ | $-$ | $50$ | $0$ | $50$ | $-$ | $-$ | $-$ | $-$     * $1$ | $30$ | $30$ | $50$ | $100$ | $150$ | $3.33$ | $1.67$ | $3.33$ | $5$     * $2$ | $50$ | $20$ | $50$ | $200$ | $250$ | $5$ | $1$ | $4$ | $5$     * $3$ | $66$ | $16$ | $50$ | $300$ | $350$ | $6.25$ | $0.76$ | $4.54$ | $5.3$     * $4$ | $80$ | $14$ | $50$ | $400$ | $450$ | $7.14$ | $0.63$ | $5$ | $5.63$     * $5$ | $92$ | $12$ | $50$ | $500$ | $550$ | $8.33$ | $0.54$ | $5.43$ | $5.98$

Cost Curves and Their Shapes

• Three Key Graphical Features:     1. Shape of the MC curve.     2. Shape of the ATC curve.     3. Relationship between MC and ATC.

• Marginal Cost (MC) Curve:     * Often U-shaped, but economists are primarily interested in the upward-sloping portion.     * Visualized as a "Nike swoosh" or a checkmark.     * Represents the slope of the TC function (increasing at an increasing rate).     * The upward slope is a direct result of diminishing marginal product.

• Average Fixed Cost (AFC) Curve:     * Always decreasing as output ($Q$) increases.     * Formulaic Reason: $AFC = \frac{\text{constant value}}{\text{increasing value}} \implies AFC \text{ falls with } Q$.

• Average Variable Cost (AVC) Curve:     * U-shaped.     * Reflects diminishing marginal product.

• Average Total Cost (ATC) Curve:     * U-shaped.     * ATC > AVC always because $ATC = AFC + AVC$.     * ATC starts high at low levels of output due to very high AFC.     * Eventually, rising AVC becomes the dominant force, causing ATC to start rising.

The Marginal-Average Relationship

• Analogy: Test Scores and Averages:     * (1) Liam: Marginal Score $80$; Total $80$; Average $80$.     * (2) Sophia: Marginal Score $70$; Total $150$; Average $75$ (Marginal < Average; Average pulled DOWN).     * (3) Noah: Marginal Score $66$; Total $216$; Average $72$ (Marginal < Average; Average pulled DOWN).     * (4) Olivia: Marginal Score $68$; Total $284$; Average $71$ (Marginal < Average; Average pulled DOWN. Note: Marginal went up from previous score, but is still below the average).     * (5) Jackson: Marginal Score $76$; Total $360$; Average $72$ (Marginal > Average; Average pulled UP).     * (6) Emma: Marginal Score $90$; Total $450$; Average $75$ (Marginal > Average; Average pulled UP).     * (7) Elijah: Marginal Score $75$; Total $525$; Average $75$ (Marginal = Average; Average UNCHANGED).

• Rules of Thumb for Cost:     * If MC < ATC, then ATC is falling (pulled DOWN).     * If MC > ATC, then ATC is rising (pulled UP).     * If $MC = ATC$, ATC is unchanged. This occurs at the minimum of the U-shaped ATC curve.     * Efficient Scale: The quantity of output that minimizes Average Total Cost.

Costs in the Short Run and Long Run

• Short Run (SR):     * At least one factor of production is fixed (usually capital, such as the size of the facility).     * The firm is "fixed" to one of its SR cost curves.

• Long Run (LR):     * All costs are variable; there are no fixed costs.     * A firm can choose to operate on any of its SR ATC curves.     * The LR ATC curve is much flatter than the SR ATC curves and lies below (or equal to) the SR curves.

• Long Run Economies of Scale:     * Economies of Scale: LR ATC is decreasing as output increases. This is often due to increased specialization.     * Constant Economies (or Returns) to Scale: LR ATC remains unchanged as output increases.     * Diseconomies of Scale: LR ATC is increasing as output increases. This is often due to coordination problems.