Micro Week 1 seminar Profit Maximization and Competitive Supply

Perfectly Competitive Markets

Perfect competition rests on three basic assumptions: price taking, product homogeneity, and free entry and exit. Individual firms act as price takers because each sells a small proportion of overall market output and cannot influence the market price. Product homogeneity ensures that products are perfect substitutes, establishing a single market price. Free entry and exit means firms face no special costs when entering or leaving an industry, allowing buyers to switch suppliers easily.

Profit Maximization and Marginal Revenue

Firms choose output levels to maximize total profit, defined as the difference between total revenue and total cost. Profit is maximized at an output level $q^*$ where marginal revenue equals marginal cost. For a price-taking firm in a perfectly competitive market, the demand curve facing the firm is horizontal, meaning price, average revenue, and marginal revenue are all equal. Thus, the competitive firm maximizes profit by choosing output where $MC(q) = MR = P$.

Short-Run Output and Shutdown Decisions

In the short run, a competitive firm maximizes profit at the output level where $MC = P$, provided price exceeds average variable cost ($AVC$). If price falls below $AVC$, the firm minimizes losses by shutting down completely, producing zero output. If price is above $AVC$ but below average total cost ($ATC$), the firm continues to operate in the short run despite incurring losses, as revenue covers all variable costs and a portion of fixed costs.

Short-Run Supply Curves

A competitive firm's short-run supply curve is the portion of its marginal cost curve that lies above its average variable cost curve. An increase in input price shifts the marginal cost curve upward from $MC_1$ to $MC_2$, reducing the profit-maximizing output level from $q_1$ to $q_2$. The short-run market supply curve is the horizontal summation of individual firm supply curves. Market elasticity of supply is calculated as $E_s = \frac{\Delta Q / Q}{\Delta P / P}$.

Empirical Cost and Supply Decisions

Industrial operations demonstrate varying short-run cost structures and supply elasticity. An aluminum smelting plant produces $600\,\text{tons per day}$ at prices between $\\n1140$ and $\\n1300\,\text{per ton}$, increasing to $900\,\text{tons per day}$ via overtime shifts when prices exceed $\\n1300\,\text{per ton}$. In world copper production, marginal costs vary across nations, ranging from a low of $\\n1.30\,\text{per pound}$ in Russia to a high of $\\n2.60\,\text{per pound}$ in Canada, causing the global supply curve to slope upward and become increasingly inelastic as output approaches maximum production capacity.

Perfectly Competitive Markets

• Price Taker: A firm that has no influence over market price and thus takes the market price as given, because each individual firm sells a small proportion of overall market output.

• Product Homogeneity: When the products of all firms in a market are perfectly substitutable with one another (homogeneous), establishing a single market price.

• Free Entry and Exit: A condition under which there are no special costs that make it difficult for a firm to enter or exit an industry, allowing buyers to switch suppliers easily.

Profit Maximization and Marginal Revenue

• Profit: The difference between total revenue ($R$) and total cost ($C$).

• Marginal Revenue ($MR$): The change in revenue resulting from a one-unit increase in output.

• Marginal Cost ($MC$): The change in cost resulting from a one-unit increase in output.

• Profit Maximization Rule: Profit is maximized at an output level $q^*$ where marginal revenue equals marginal cost ($MR = MC$).

• Competitive Demand Curve: For a price-taking firm in a perfectly competitive market, the demand curve facing the firm is horizontal (perfectly elastic), meaning price ($P$), average revenue ($AR$), and marginal revenue ($MR$) are all equal ($MC(q) = MR = P$).

Short-Run Output and Shutdown Decisions

• Short-Run Profit Maximization: In the short run, a competitive firm maximizes profit at the output level where $MC = P$, provided price exceeds average variable cost ($AVC$).

• Shutdown Decision: If price falls below average variable cost ($AVC$), the firm minimizes losses by shutting down completely, producing zero output.

• Operating at a Loss: If price is above average variable cost ($AVC$) but below average total cost ($ATC$), the firm continues to operate in the short run despite incurring losses, as revenue covers all variable costs and a portion of fixed costs.

Short-Run Supply Curves

• Firm Supply Curve: A competitive firm's short-run supply curve is the portion of its marginal cost ($MC$) curve that lies above its average variable cost ($AVC$) curve.

• Input Price Changes: An increase in input price shifts the marginal cost curve upward from $MC<em>1$ to $MC</em>2$, reducing the profit-maximizing output level from $q<em>1$ to $q</em>2$.

• Short-Run Market Supply Curve: The horizontal summation of individual firm supply curves.

• Market Elasticity of Supply ($E<em>s$): Calculated as $E</em>s = \frac{\Delta Q / Q}{\Delta P / P}$.

Empirical Cost and Supply Decisions

• Aluminum Smelting Plant: Demonstrates short-run output changes; produces $600\,\text{tons per day}$ at prices between $\$1140$ and $\$1300\,\text{per ton}$, and increases to $900\,\text{tons per day}$ via overtime when prices exceed $\$1300\,\text{per ton}$.

• World Copper Supply: Marginal costs range from a low of $\$1.30\,\text{per pound}$ in Russia to a high of $\$2.60\,\text{per pound}$ in Canada, causing the global supply curve to slope upward and become increasingly inelastic as output approaches maximum production capacity.