Lecture 6: Perfectly Competitive Supply and Marginal Analysis

Review of Demand Elasticity Concepts

• Determining Price Elasticity of Demand: The price elasticity of demand can be determined by knowing the following variables:     * The price.     * The quantity demanded.     * The slope of the demand curve.

• Price Movements in Elastic Regions: If a point on the demand curve currently sits in the elastic region and experiences an increase in price, the new price and quantity will be relatively more elastic.

Market Structures and Characteristics

• Market Structure Continuum: Markets are categorized based on pricing power and demand elasticity. Moving from many small firms to a single large firm, pricing power increases and demand becomes more inelastic.     * Perfectly Competitive: No pricing power; price takers.     * Monopolistic: Low pricing power.     * Oligopoly: High pricing power.     * Monopoly: Maximum pricing power.

• Features of a Perfectly Competitive Market:     * Many Buyers and Sellers: The market consists of many small participants; no single buyer or seller can dictate the market price.     * Homogeneous Products: Products are identical with no ability to differentiate; they serve as perfect substitutes for one another.     * Resource Mobility: Resources are perfectly mobile. There are no transport costs, and firms are free to enter or leave the industry.     * Easy Entry and Exit: There are no significant barriers to entry or high costs associated with exiting the industry.     * Perfect Knowledge: Both buyers and sellers have perfect information about prices and competitors within the industry.

• Market Realities: Perfectly competitive markets are often viewed as idealized abstractions. In these markets:     * Firms are price takers, meaning they must accept the price dictated by the market.     * The invisible hand and industry forces drive supply and demand toward a market-clearing point.     * Each individual firm supplies as much as it can at the market price to maximize its personal profit.

Production and Supply in the Short and Long Run

• Market Supply: This is the sum of all individual suppliers in the market. At any given price, the market quantity supplied is calculated as the sum of all individual quantities supplied by every firm at that price.

• Short Run Definitions: This is a time period where some inputs (such as capital and equipment) are fixed and cannot be changed.

• Long Run Definitions: This is a time period where all inputs can change, including technology, physical site size, and overall operations.

• Employment and Output (Short Run Pizza Shop Example):     * Observations of the Law of Diminishing Returns: Output gains from each additional worker begin to diminish starting with the third worker.     * Total Output Table:         * $0$ employees: $0$ pizzas per day ($MPL = 0$).         * $1$ employee: $80$ pizzas per day ($MPL = 80$).         * $2$ employees: $200$ pizzas per day ($MPL = 120$).         * $3$ employees: $260$ pizzas per day ($MPL = 60$).         * $4$ employees: $300$ pizzas per day ($MPL = 40$).         * $5$ employees: $330$ pizzas per day ($MPL = 30$).         * $6$ employees: $350$ pizzas per day ($MPL = 20$).         * $7$ employees: $362$ pizzas per day ($MPL = 12$).

Economic Cost Definitions and Formulas

• Total Fixed Costs (TFC): The sum of all input costs that remain constant regardless of whether output increases or decreases (e.g., rent, insurance). Measured in $.</p></li><li><p><strong>Total Variable Costs (TVC):</strong> The sum of input costs that vary directly with output levels (e.g., topping ingredients, casual wages). Buying in bulk can sometimes reduce the per-unit cost. Measured in$.

• Total Costs (TC): The sum of all costs used to produce $Q$ units. Formula: $TC = TFC + TVC$. Measured in $.</p></li><li><p><strong>Average Total Costs (ATC):</strong> The total cost per unit of output. Formula:$ATC = \frac{TC}{Q}$. Measured in$/unit$.</p></li><li><p><strong>Average Fixed Costs (AFC):</strong> The fixed cost per unit of output. Formula:$AFC = \frac{TFC}{Q}$. Measured in$/unit$.</p></li><li><p><strong>Average Variable Costs (AVC):</strong> The variable cost per unit of output. Formula:$AVC = \frac{TVC}{Q}$. Measured in$/unit$.</p></li><li><p><strong>Marginal Cost (MC):</strong> The change in total cost resulting from producing one additional unit. Formula:$MC = \frac{\Delta TC}{\Delta Q}$. Measured in$/unit.     * Example: The additional cost for a 10th space shuttle launch might be \$8$billion compared to$\$3 billion for the 2nd launch.

Case Study: Suburban Pizza Shop Analysis

• Assumptions:     1. Operations occur in the short run (shop size and number of ovens are fixed).     2. Higher output is achieved solely by hiring more casual staff (variable wage costs).

• Financial and Cost Data Table:     * Quantity (Q$) =$0$:$TFC = 120$,$TVC = 0$,$TC = 120$,$AFC = n/a$,$AVC = n/a$,$ATC = n/a$,$MC = n/a.     * Quantity (Q$) =$10$:$TFC = 120$,$TVC = 20$,$TC = 140$,$AFC = 12$,$AVC = 2$,$ATC = 14$,$MC = 2.     * Quantity (Q$) =$20$:$TFC = 120$,$TVC = 30$,$TC = 150$,$AFC = 6$,$AVC = 1.5$,$ATC = 7.5$,$MC = 1.     * Quantity (Q$) =$30$:$TFC = 120$,$TVC = 50$,$TC = 170$,$AFC = 4$,$AVC = 1.7$,$ATC = 5.7$,$MC = 2.     * Quantity (Q$) =$40$:$TFC = 120$,$TVC = 80$,$TC = 200$,$AFC = 3$,$AVC = 2$,$ATC = 5$,$MC = 3.     * Quantity (Q$) =$50$:$TFC = 120$,$TVC = 130$,$TC = 250$,$AFC = 2.4$,$AVC = 2.6$,$ATC = 5$,$MC = 5.     * Quantity (Q$) =$60$:$TFC = 120$,$TVC = 230$,$TC = 350$,$AFC = 2$,$AVC = 3.8$,$ATC = 5.83$,$MC = 10.     * Quantity (Q$) =$70$:$TFC = 120$,$TVC = 380$,$TC = 500$,$AFC = 1.7$,$AVC = 5.4$,$ATC = 7.1$,$MC = 15.     * Quantity (Q$) =$80$:$TFC = 120$,$TVC = 690$,$TC = 810$,$AFC = 1.5$,$AVC = 8.6$,$ATC = 10.1$,$MC = 31$.</p></li></ul><h3 id="57186503-9ecb-44d6-a454-230c49d895ca" data-toc-id="57186503-9ecb-44d6-a454-230c49d895ca" collapsed="false" seolevelmigrated="true">Profit Maximization Strategies</h3><ul><li><p><strong>Profit Calculation:</strong>$\text{Profit} = \text{Revenue} - \text{Expenses}$.</p></li><li><p><strong>Revenue Calculation:</strong>$\text{Revenue} = \text{Price} \times \text{Quantity}.

• Marginal Analysis for Profit: To maximize profit, a firm must evaluate the incremental revenue (Marginal Revenue) against the incremental cost (Marginal Cost) of producing one more unit.     * If MR > MC, the firm should produce the unit as it provides an incremental increase to total profit.     * The general rule for profit maximization in a competitive market is to produce output until the point where Price = Marginal Cost$($P = MC ).     * For a perfectly competitive firm, Demand is perfectly elastic (horizontal), so Price = MR$. Thus, the rule is also expressed as$MR = MC$.</p></li><li><p><strong>Firm Supply Curve:</strong> In the short run, the Marginal Cost ($MC$) curve is effectively the supply curve ($S_{firm}$) for an individual firm.</p></li></ul><h3 id="1113b112-3c2c-4cd5-994d-6a90f66bb087" data-toc-id="1113b112-3c2c-4cd5-994d-6a90f66bb087" collapsed="false" seolevelmigrated="true">Graphical Solutions and Market Outcomes</h3><ul><li><p><strong>Economic Profit Scenario:</strong> If the market price is$\$10:     1. Set P = MC$($10 = 10$at$Q = 60 pizzas).     2. Revenue = \$10 \times 60 = \$600.     3. Total Cost = ATC \times Q = 5.83 \times 60 = \$350.     4. Economic Profit = \$600 - \$350 = \$250$.</p></li><li><p><strong>Zero Economic Profit (Break-even):</strong> Occurs when Price equals the minimum of the Average Total Cost ($ATC).     * If Price = \$5$and$ATC = \$5$at$Q = 50$, then Revenue ($\$250$) minus Total Cost ($\$250$) equals$\$0$economic profit.</p></li><li><p><strong>Loss Minimization:</strong> This occurs when$AVC < Price < ATC.     * Revenue covers all variable costs and a portion of the fixed costs.     * Example: Price = \$3$,$ATC = \$5$,$AVC = \$2$at$Q = 40$. The fixed cost is$\$120$. Revenue covers the$\$80$variable cost and contributes towards the fixed cost, resulting in an economic loss of$\$80$(as opposed to a$\$120$loss if the shop closed immediately).</p></li><li><p><strong>Shutdown Point:</strong> If the market price falls below the minimum point of the Average Variable Cost ($AVC$) curve ($Price < \text{min } AVC), the firm should shut down immediately.     * Revenue cannot cover even the variable costs (like casual wages).     * Example: Price = \$1.50$and min$AVC = \$1.50$at$Q = 25. At this point, none of the fixed costs are covered, and it is more efficient to leave the industry and use resources elsewhere.

Questions & Discussion

• Q: What price do you charge per pizza?

• A: In a perfectly competitive market, the price is dictated by the market clearing point determined by industry-wide supply and demand. The individual firm is a price taker.

• Q: How many pizzas need to be sold to maximize profit?

• A: Production should continue until Marginal Revenue equals Marginal Cost (MR = MC$). For the suburban pizza shop case with a price of$\$10$$, this occurs at 60 pizzas.

• Q: Will a business survive a loss-minimizing state?

• A: Survival is possible in the short run if variable costs are met, but not sustainable in the long run if total costs exceed total revenue.

• Q: What happens when new players enter the industry?

• A: When initial firms make high economic profits, new players enter the industry, which increases supply and causes profits to be competed away.