Microeconomics Study Notes: Cost of Production, Profit Maximization, and Competitive Markets

Chapter 7: The Cost of Production

7.3 Cost in the Long-Run

The long-run cost analysis examines how firms choose input combinations and minimize costs when all inputs are variable. Key concepts include the user and rental cost of capital, isocost lines, and the firm's expansion path.

• User Cost of Capital: The total annual cost of owning and using a capital asset, including depreciation and the opportunity cost of funds tied up in the asset.

• Rental Cost of Capital: The cost of renting a unit of capital for a specified period, reflecting both depreciation and the required return on investment.

• Isocost Line: A line representing all combinations of inputs (e.g., labor and capital) that cost the same total amount. The equation for an isocost line is: $C = wL + rK$ where $C$ is total cost, $w$ is the wage rate, $L$ is labor, $r$ is the rental rate of capital, and $K$ is capital.

• Cost Minimization Condition: To produce a given output at minimum cost, the firm chooses input levels such that: $\frac{MP_L}{MP_K} = \frac{w}{r}$ where $MP_L$ and $MP_K$ are the marginal products of labor and capital, respectively.

• Firm’s Expansion Path: The locus of cost-minimizing input combinations as output varies, holding input prices constant. It shows how the optimal mix of inputs changes as the firm expands production.

• Deriving Long-Run Costs: The long-run cost curve is derived from the expansion path by plotting the minimum cost for each output level.

7.4 Long-Run versus Short-Run Cost Curves

Understanding the relationship between long-run and short-run cost curves is essential for analyzing firm behavior and market supply.

• Long-Run Average Cost (LRAC) Curve: Shows the lowest possible average cost of production, allowing all inputs to vary. It is typically U-shaped due to economies and diseconomies of scale.

• Short-Run Average Cost (SRAC) Curve: Shows average cost when at least one input is fixed. Each SRAC curve corresponds to a different level of fixed input.

• Relationship: The LRAC curve is the lower envelope of all possible SRAC curves.

• Economies of Scale: Occur when increasing output leads to a lower average cost ($LRAC$ declines as output increases).

• Diseconomies of Scale: Occur when increasing output raises average cost ($LRAC$ rises as output increases).

• Increasing Returns to Scale vs. Economies of Scale: Increasing returns to scale refers to output increasing more than proportionally with input increases (a technological concept), while economies of scale refer to declining average costs (a cost concept). They often coincide but are not identical.

• Cost Output Elasticity: Measures the percentage change in cost resulting from a one percent change in output: $E_C = \frac{\%\,\Delta C}{\%\,\Delta Q}$ If $E_C < 1$, there are economies of scale; if $E_C > 1$, diseconomies of scale.

7.5 Production with Two Outputs – Economies of Scope

Firms may produce multiple outputs, leading to potential cost savings known as economies of scope.

• Economies of Scope: Exist when it is less costly to produce two or more products together than separately. The degree of economies of scope is measured as: $SC = \frac{C(Q_1, 0) + C(0, Q_2) - C(Q_1, Q_2)}{C(Q_1, Q_2)}$ where $C(Q_1, Q_2)$ is the cost of producing quantities $Q_1$ and $Q_2$ jointly.

• Diseconomies of Scope: Occur when joint production is more costly than separate production.

Chapter 8: Profit Maximization and Competitive Supply

Characteristics of a Perfectly Competitive Market

Perfect competition is a market structure with many buyers and sellers, homogeneous products, and free entry and exit.

• Key Features:

  • Many firms and buyers

  • Identical (homogeneous) products

  • Perfect information

  • No barriers to entry or exit

  • Firms are price takers

Output Decision of a Perfectly Competitive Firm

A competitive firm chooses output to maximize profit, taking the market price as given.

• Profit Maximization Rule: The firm produces where marginal cost equals market price: $P = MC$

• Graphical Approach: The profit-maximizing output is where the marginal cost curve intersects the market price line (which is also the marginal revenue for a competitive firm).

• Demand and Marginal Revenue: For a competitive firm, the demand curve is perfectly elastic at the market price, and marginal revenue equals price ($MR = P$).

Short-Run Output Choice and Shut Down Decision

• Short-Run Output Choice: The firm produces where $P = MC$ as long as price covers average variable cost ($P \geq AVC$).

• Shut Down Decision: If $P < AVC$, the firm shuts down in the short run.

Short-Run Supply Curve

• Firm’s Short-Run Supply Curve: The portion of the marginal cost curve above the average variable cost curve.

• Market Short-Run Supply: The horizontal sum of all individual firms’ supply curves.

Long-Run Output Choice and Industry Supply

• Long-Run Output Choice: Firms enter or exit the market until economic profit is zero ($P = LRAC$).

• Industry Long-Run Supply Curve:

  • Constant Cost Industry: Entry or exit does not affect input prices; the long-run supply curve is horizontal.

  • Increasing Cost Industry: Entry raises input prices; the long-run supply curve slopes upward.

  • Decreasing Cost Industry: Entry lowers input prices; the long-run supply curve slopes downward.

Chapter 9: The Analysis of Competitive Markets

Evaluating Gains and Losses from Government Policies

Government interventions affect market outcomes, leading to changes in consumer and producer surplus, welfare, and deadweight loss.

• Consumer Surplus: The difference between what consumers are willing to pay and what they actually pay.

• Producer Surplus: The difference between the price producers receive and the minimum they would accept.

• Welfare Effects: The overall impact on economic well-being, including changes in consumer and producer surplus and government revenue.

• Deadweight Loss: The loss of total surplus due to market distortions (e.g., taxes, price controls).

Efficiency of Competitive Markets

• Competitive markets maximize total surplus and allocate resources efficiently, assuming no externalities or market failures.

Price Ceilings and Price Floors

• Price Ceiling: A legal maximum price. If set below equilibrium, it causes shortages and deadweight loss.

• Price Floor: A legal minimum price. If set above equilibrium, it causes surpluses and deadweight loss.

• Welfare Effects: Both policies create winners and losers and reduce total surplus.

Production Quotas, Import Quotas, and Tariffs

• Production Quota: A limit on the quantity a firm or industry can produce, typically raising prices and reducing welfare.

• Import Quota: A limit on the quantity of a good that can be imported.

• Tariff: A tax on imported goods, raising domestic prices and generating government revenue but causing deadweight loss.

Impact of a Tax or Subsidy

• Tax Incidence: The division of the tax burden between buyers and sellers, determined by the relative elasticities of supply and demand.

• Elasticity and Tax Incidence: The side of the market (buyers or sellers) that is less elastic bears more of the tax burden.

• Deadweight Loss: Taxes create deadweight loss by reducing the quantity traded below the efficient level.

• Government Revenue: Equal to the tax per unit times the quantity sold after the tax.

• Price Effects: Taxes raise the price consumers pay and lower the price suppliers receive.

• Graphical Analysis: Used to illustrate the effects of taxes and subsidies on equilibrium price, quantity, and welfare.