Sellers and Incentives

Introduction

This chapter explores how market incentives influence a firm's decision regarding the quantity of goods to produce. The central problem for firms is to select a production quantity that maximizes economic profits, given prices and production technologies. Marginal analysis is used to determine the profit-maximizing output, and the optimal quantity is where marginal benefit (MB) equals marginal cost (MC) for the last unit produced. Production decisions differ between the short-run and long-run, and once a firm's supply curve is derived, concepts such as producer surplus and price elasticity of supply can be analyzed.

Key Terms and Definitions

• Firm: An economic unit that produces goods or services for sale.

• Production: The process of transforming inputs (factors of production) into outputs.

• Physical capital (K): Man-made resources like machines and buildings.

• Labor (L): Human effort used in production.

• Land (T): Natural resources used in production.

• Short-run: A period in which at least one factor of production is fixed.

• Long-run: A period in which all factors of production are variable.

• Fixed factor of production: An input that cannot be changed in the short-run.

• Variable factor of production: An input that can be changed in the short-run.

• Marginal product (MP): The additional output produced by employing one more unit of input.

• Specialization: Focusing on a specific task to increase efficiency.

• Law of diminishing returns: As more of a variable input is added to a fixed input, the marginal product eventually decreases.

• Cost of production: The total expenses incurred in producing goods.

• Total cost (TC): The sum of all costs incurred in production.

• Variable cost (VC): Costs that change with the level of output.

• Fixed cost (FC): Costs that do not change with the level of output.

• Average total cost (ATC): Total cost divided by the quantity produced.

• Average variable cost (AVC): Variable cost divided by the quantity produced.

• Average fixed cost (AFC): Fixed cost divided by the quantity produced.

• Marginal cost (MC): The increase in total cost from producing one more unit.

• Revenue: Income from selling goods or services.

• Marginal revenue (MR): The additional revenue from selling one more unit.

• Profits (Π): The difference between revenue and costs.

• Accounting profits: Revenue minus explicit accounting costs.

• Economic profits: Revenue minus accounting costs and opportunity costs.

• Price elasticity of supply: The responsiveness of quantity supplied to changes in price.

• Shutdown: A short-run decision to stop production when revenue cannot cover variable costs.

• Sunk costs: Costs that cannot be recovered once incurred.

• Producer surplus: The difference between the price received and the minimum willingness to accept.

• Economies of scale: Decreasing average costs as production increases.

• Constant returns to scale: Average costs remain unchanged as production increases.

• Diseconomies of scale: Increasing average costs as production increases.

• Exit: Leaving the market in the long-run when profits are negative.

• Free entry: The ability for new firms to enter the market without barriers.

• Subsidy: Financial assistance to firms to encourage production.

Perfectly Competitive Market

Characteristics

• Many buyers and sellers.

• Homogeneous products (perfect substitutes).

• Buyers and sellers are price takers; no individual can influence the market price.

• Free entry and exit in the market.

• In long-run equilibrium, all firms earn zero economic profit (assuming identical cost structures).

The Seller's Problem

Elements of the Seller's Problem

• Production: How inputs are transformed into outputs.

• Cost of Doing Business: The expenses incurred in production.

• Rewards of Doing Business: The revenue received from selling goods.

Profit is defined as:

Production Time Horizons

• Short-run: At least one input is fixed.

• Long-run: All inputs are variable.

Marginal Product and Returns

• Marginal Product (MP): where

• Increasing returns (specialization): MC decreases as output increases.

• Diminishing returns: MC increases as output increases due to capacity constraints.

Example: Production of Cheese Boxes

Over 0-4 workers: increasing returns; MC decreases. Over 5+: diminishing returns; MC increases.

Costs of Production

• Short-run:

• Long-run:

• Variable costs depend on output; fixed costs do not.

Cost Function Example

Given , the fixed cost is 100, and the variable cost is . This is a short-run cost function.

Average Costs

• Average Total Cost (ATC):

• Average Fixed Cost (AFC):

• Average Variable Cost (AVC):

Relationships Between MC, ATC, AVC, and AFC

• MC intersects ATC and AVC at their minimum points.

• If MC < ATC, ATC is decreasing; if MC > ATC, ATC is increasing.

• AFC approaches zero as output increases.

Revenue and Marginal Revenue

• Revenue:

• Marginal Revenue (MR): (in perfect competition)

• Firm's demand curve is perfectly elastic:

Profit Maximization

• Firm maximizes profit where and (short-run), (long-run).

• Economic profit:

• Accounting profit:

Example Calculation

• Given , ,

• Set :

• Profit:

Short-run Production Decision Rules

• Produce where as long as .

• If , (loss equals fixed costs).

• Shutdown if ; shutdown point is where (minimum AVC).

From Seller's Problem to the Supply Curve

Deriving the Supply Curve

• The supply curve shows the quantity a firm is willing to supply at each price.

• Short-run supply curve: MC curve above minimum AVC.

• Shutdown point: ; firm is indifferent between producing and shutting down.

Sunk Costs

• Sunk costs are not considered in the firm's production decision.

• Only current and future costs matter for decision-making.

Price Elasticity of Supply

Definition and Calculation

• Price elasticity of supply:

• Arc elasticity formula:

Interpreting Elasticities

• : Perfectly elastic supply.

• : Unit elastic supply.

• : Perfectly inelastic supply.

• : Inelastic supply.

• : Elastic supply.

Producer Surplus

Definition and Calculation

• Producer surplus (PS): The difference between the price received and the minimum willingness to accept (WTA).

• PS is the area below price and above the supply (MC) curve up to the quantity sold.

Example: Shoes

• Sold for PS = 75 - 50 = 25 $

Graphical Example: Oranges Market

• Market price , oranges.

• PS for 25th orange:

• Market PS:

From the Short-Run to the Long-Run

Production in the Long-Run

• All factors of production are variable.

• Total costs = variable costs.

• Firm produces if ; otherwise, it exits the market.

• Long-run supply: MC curve above minimum ATC.

Deriving the Long-run ATC Curve

• Firms choose the lowest-cost alternative for each output level.

• Long-run ATC lies below the minimum points of all short-run ATC curves.

Economies, Constant Returns, and Diseconomies of Scale

• Economies of scale: Average costs decrease as production increases (for ).

• Constant returns to scale: Average costs remain unchanged as production increases (minimum efficient scale).

• Diseconomies of scale: Average costs increase as production increases (for ).

Long-Run Competitive Equilibrium

Market Dynamics

• In long-run equilibrium, all firms earn zero economic profit.

• No incentive for entry or exit.

• If : Firms enter, supply increases, price falls, profits return to zero.

• If : Firms exit, supply decreases, price rises, profits return to zero.

• Long-run market supply curve is perfectly elastic.

Summary Table: Short-run vs Long-run Production Decisions

Summary

• The firm's problem is to determine the profit-maximizing quantity given price and production technology.

• Quantity supplied is where .

• Short-run: produce if ; long-run: produce if .

• Supply curve: MC above minimum AVC (short-run), MC above minimum ATC (long-run).

• Long-run equilibrium: zero economic profit due to free entry and exit.