Profit Maximisation and Firm Behavior in Output Markets

Organizational Structure and the Make or Buy Decision

• Firms continuously strive for an optimal combination of internal transactions (those occurring within the firm) and external transactions (those occurring on the market).

• The fundamental question facing every firm is the make or buy decision, also referred to as outsourcing. This involves determining whether it is more efficient to produce a good or service internally or to purchase it from the market.

• Case Study: Volvo Car Gent

  • As an organization, Volvo coordinates approximately $7000$ direct employees who manage tasks related to the assembly of new passenger cars.

  • Volvo outsources the production of many parts to other firms.

  • Many suppliers are located in the immediate vicinity of the assembly plant.

  • Parts are delivered in the exact order in which they are to be installed, which significantly reduces stock levels and transport costs.

  • Since most cars are made to order with varying options, coordinating this logistical flow is complex.

  • It is considered optimal for Volvo Car Gent to outsource part production while maintaining significant transaction-specific investments internally.

Economic Gains and Profit Maximization

• Profit is defined as the difference between a firm's total revenues and its total costs.

• Total Revenues: Primary income derived from sold output.

• Total Costs: Expenditure on factors of production (labour and capital) and inputs (raw materials and energy).

• Economic Profit: The difference between total economic revenue and total economic cost.

• Economic Cost (Opportunity Cost): The value of an input in its best alternative use. This often differs from the accounting cost found in financial statements.

• Example: Newspaper Retailer

  • Turnover: $\text{€}170,000$.

  • Purchases (Newspapers, etc.): $\text{€}80,000$.

  • Staff Wages/Social Contributions: $\text{€}50,000$.

  • Accounting Profit: $\text{€}170,000 - (\text{€}80,000 + \text{€}50,000) = \text{€}40,000$.

  • Uncounted Economic Factors:

    1. The owner’s labor: If she could earn $\text{€}40,000$ elsewhere, this represents an attributed salary cost.

    2. Physical Capital: If the building (wholly owned) could be rented for $\text{€}10,000$, this is an allocated rent cost.

  • Total Economic Cost: $\text{€}130,000 + \text{€}40,000 + \text{€}10,000 = \text{€}180,000$.

  • Economic Profit: $\text{€}170,000 - \text{€}180,000 = -\text{€}10,000$.

• Example: Coffee Roaster

  • A roaster has a long-term contract to buy beans at $\text{€}5$ per kilo.

  • The market price drops to $\text{€}4$ per kilo.

  • While the accounting cost is $\text{€}5$, the opportunity cost (the current resale value) is $\text{€}4$. This current price of $\text{€}4$ should drive output and pricing decisions.

Short-Run vs. Long-Run Time Horizons

• Short Run: A period during which some factors of production are fixed and cannot be changed.

  • For car manufacturers, capital goods like machinery and buildings are fixed.

  • Sudden demand increases are met by variable factors like labour (overtime or extra shifts).

  • Sudden demand drops are constrained by ongoing rental contracts.

  • The duration varies by industry: a consultant's short run may be days, while a nuclear power plant's short run may be several years.

• Long Run: A period where the firm is no longer hampered by adjustment costs or fixed factors. All inputs are variable.

• In the long run, analysis must account for the free entry and exit of firms. Profits attract new entrants, while losses lead to the disappearance of existing firms.

Revenues and Costs in the Sandwich Shop Example

• Demand Curves:

  • The firm's demand curve, denoted as $q(p)$, is typically smaller and flatter than the market demand curve ($D(p)$) because of substitutes.

  • In a monopoly, the firm's demand coincides with market demand.

  • In perfect competition, the demand curve is horizontal because firms are price takers.

  • Sandwich Shop Demand: $q(p) = 600 - 100p$.

  • Inverse Demand Curve: $p(q) = 6 - 0.01q$.

• Total Revenue (TR):

  • $TR(q) = p(q)q$.

  • An increase in output increases revenue directly but reduces the price required to sell that output.

  • TR Function: $TR(q) = 6q - 0.01q^2$.

  • Maximal revenue for the sandwich shop is $\text{€}900$ at $300$ sandwiches.

• Average Revenue (AR):

  • $AR(q) = \frac{TR(q)}{q} = p(q)$. AR is equal to the price.

• Marginal Revenue (MR):

  • The derivative of total revenue to output: $MR(q) = \frac{dTR(q)}{dq}$.

  • MR Function: $MR(q) = 6 - 0.02q$.

  • MR is lower than the price for all units except the first because the lower price applies to all units sold.

Cost Functions and Algebraic Relationships

• Total Cost (TC):

  • Example: $TC(q) = 0.0001 - 0.045q^2 + 8q$.

• Average Cost (AC):

  • $AC(q) = \frac{TC(q)}{q} = 0.0001q^2 - 0.045q + 8$.

  • Graphically, AC is the slope of the line through the origin to a point on the TC curve. It is U-shaped.

• Marginal Cost (MC):

  • The change in total costs for a very small change in output: $MC(q) = \frac{dTC(q)}{dq}$.

  • MC Function: $MC(q) = 0.0003q^2 - 0.09q + 8$.

  • MC is represented by the slope of the tangent to the TC curve and is also U-shaped.

• Link Between Average and Marginal Values:

  • An average increases only if the marginal value is higher than the average.

  • An average decreases if the marginal value is lower than the average.

  • Average costs reach a minimum when $MC = AC$.

Behavioural Rules for Profit Maximization

• Profit Function: $\Pi(q) = TR(q) - TC(q)$.

• The Output Rule:

  • To maximize profit, a firm chooses output level $q^*$ where $MR(q^*) = MC(q^*)$.

  • As long as $MR > MC$, marginal profit is positive, and the firm should produce more.

  • If $MC > MR$, the firm should produce less.

• Numerical Data for Output Rule (Table 8.4 Highlights):

  • At $q = 150$: $MR = 3$, $MC = 1.25$, Marginal Profit = $1.75$.

  • At $q = 200$: $MR = 2$, $MC = 2$, Marginal Profit = $0$. (Profit is maximal at $\text{€}200$).

  • At $q = 250$: $MR = 1$, $MC = 4.25$, Marginal Profit = $-3.25$.

• The Shutdown Rule (Long Run):

  • A firm will shut down if the highest possible profit in case of production is smaller than the profit from not producing (zero).

  • Algebraically: $\Pi(q^*) < 0$.

The Supply of Competitive Firms

• In perfect competition, firms are price takers with horizontal demand ($AR = MR = p$).

• Output Rule for Competitive Firms: Choose output such that $p = MC(q^*)$.

• Shutdown Rule for Competitive Firms: Shut down if $p < AC(q^*)$.

• Individual Supply Curve:

  • Zero supply if the market price is below the minimum of the AC-curve.

  • If price is above the minimum of the AC-curve, supply follows the MC-curve.

• Long-Term Market Equilibrium Conditions:

  1. Price equals marginal cost ($p = MC$).

  2. Market clears (Market supply equals market demand).

  3. Price equals the minimum average cost ($p = \text{min}(AC)$), meaning zero economic profit.

Heterogeneous Firms and Economic Rent

• Identical firms lead to a perfectly elastic (horizontal) market supply curve in the long run.

• Heterogeneous firms (differing in technology, management, or location) result in a rising market supply curve.

• Most efficient firms enter the market first. As demand rises, less efficient firms enter.

• Economic Rent: Inframarginal entrants (more efficient ones) earn profit even at equilibrium prices where the marginal entrant breaks even. This profit is based on access to scarce technologies or resources.

Case Study: Paul Feldman and the Bagel Business

• Paul Feldman (analyzed by Steven Levitt) sold bagels at $\text{€}1$ via a closed box.

• Marginal Cost: $\text{€}0.37$ (wholesale price in 2005).

• Expected Marginal Revenue Calculation:

  • Price: $\text{€}1$.

  • Probability of payment: $86\%$.

  • Probability of sale (sold out frequency): $38\%$.

  • $MR = 1 \times 0.86 \times 0.38 = 0.33$.

• Because $MR (0.33)$ was close to $MC (0.37)$, Feldman approximated the profit-maximizing output. He delivered about one bagel too many on average.

• Feldman scored less well on pricing decisions; it escaped him that a higher margin could have increased profit by $30\%$.

Short-Run Production at a Loss

• Firms like dairy farmers or pig farmers often produce at a loss. This is rational in the short run due to fixed costs (FC).

• Short-Term Total Cost: $TC_{SR}(q) = VC_{SR}(q) + FC$.

• Short-Run Shutdown Rule: Shut down ONLY if profit from production is less than profit from shutdown (which is $-FC$).

  • Condition: $TR(q) - VC_{SR}(q) - FC < -FC$.

  • Simplified: $p < AVC_{SR}(q)$.

• A firm will continue to produce if the price covers at least the average variable cost ($AVC_{SR} < p$), even if total average costs ($AC_{SR}$) are not covered.

Management Theories and the Principal-Agent Problem

• Large firms exhibit a separation of ownership (shareholders) and control (management).

• The Principal-Agent Problem: Shareholders (Principals) want profit maximization. Managers (Agents) may have different objectives:

  • Prioritizing time off or leisure (e.g., golfing).

  • Valuing in-kind benefits (expensive desks, subordinate staff).

  • Seeking prestige through revenue maximization or excessive growth/acquisitions.

• Internal Control Mechanisms:

  • Direct Control: Board of directors hiring/firing management. Limited by information deficits.

  • Indirect Control (Incentives): Variable bonuses and stock options. These can lead to short-termism or free-rider problems among managers.

• External Control Mechanisms:

  • Market for Corporate Control: Poor performance leads to a drop in share price, making a hostile takeover likely. New management is then installed to raise the share value.

  • Poison Pills: Mechanisms like converting bonds to shares to deter acquirers.

  • Free-rider Problem in Takeovers: Individual shareholders may refuse to sell at a low price, waiting for the price to rise after the takeover, which disincentivizes the acquirer.

  • Product Market Competition: Highly competitive markets penalize poor decisions. Profitable firms survive because they have more resources for cost-cutting, research, and development.