Intermediate Microeconomics Lecture Notes - Profit Maximisation and Cost Functions

EC 202: Intermediate Microeconomics - Detailed Notes

Lecture Overview

• Date: Autumn 2024
• Chapters: 20 and 23 from Varian

Recap of Previous Lecture

• Discussed cost minimisation given output and technology.
• Differentiated between short-run and long-run cost functions.
• Derived conditional demands for factors leading to the (Minimum) Cost Function.
• Today's focus: profit maximisation and its relation to cost minimisation.
• Keywords: marginal cost, average cost, conditional demands for factors, cost function.

Economic Profit

• Definition: Economic profit is calculated as the difference between total revenue and total costs:
  $\Pi = R - C$

  • For a firm producing a single output (e.g., $q = 1$), with factors of production (labour $L$ and capital $K$).
    $\Pi = R - (C<em>L \times L + C</em>K \times K)$

• Breakdown of Economic Profit:

  • $R$: Total Revenue
  • $C<em>L$ and $C</em>K$: costs associated with factors of production

• Technological Constraints:

  • Summarised as: $q = f(L, K)$
  • Related concepts include:
  • Law of decreasing marginal returns (short-run)
  • Returns to scale (long-run)
  • Elasticity of substitution (long-run)

• Economic costs differ from accounting costs as they include opportunity costs associated with all resource use.

Profit Maximization

• Condition for maximising profit:
  • At maximum profit, slope of revenue $\frac{dR}{dq}$ equals slope of cost $\frac{dC}{dq}$:
    $\frac{dR}{dq} = \frac{dC}{dq}$

Profits under Perfect Competition

• Profit: $\Pi = R - C$
• Characteristics of a competitive market:
  1. Many small buyers and sellers.
  2. Firms sell identical products.
  3. Full information about product and pricing.
  4. No transaction costs.
  5. Free entry and exit into the market.
• Examples: Soybean farmers, Granny Smith apples, FloraHolland flower auctions.
• Implication: Each firm is a price-taker with a horizontal demand curve.

Conditions for Profit Maximization in a Competitive Market

• Since firms cannot influence market prices, they must choose output level $q^*$ to maximize profits:

  $\Pi = R(q) - C(q)$

• The firm sets price equal to marginal cost to produce a positive quantity.

• The shutdown point indicates the minimum price at which the firm operates.

Graphical Analysis of Profit and Cost Curves (Short-Run)

• Understanding average cost (AC), average variable cost (AVC), marginal cost (MC) relations:
  • Determine optimal quantities and profits visually.

Shutdown Decision

• Firm operates only if it yields non-negative economic profits:
  $\Pi \geq 0\implies R \geq C$

• In competitive conditions:

  • If market price p < AVC, the firm produces zero.
  • Short-Run Exclusion of fixed costs as they are not opportunity costs.

Long-Run Shutdown Decision

• Firms exit the market if price falls below average costs in the long run.

Supply Functions of Price-Taking Firms

• The supply function provides output levels at any given price ($p$).
• Operate where marginal revenue equals marginal cost:
  $p = MC$
• Shutdown condition: in short-run $p \geq min AVC$; in long-run $p \geq min AC$.

Comparing Long-Run and Short-Run Supply Functions

• Long-run supply functions can adjust input combinations more flexibly compared to short-run:
  • Elasticity and fixed factors influence comparisons between short-run and long-run costs.

Firm Behavior in Fluctuating Markets

• Oil production as a practical example of responses to price changes over time.

Rational Firm Behavior in Long-Run vs Short-Run

• Firms manage production output decisions to align with both short- and long-term goals, revealing coherence in operational strategies.

Profit Function and Factor Demands

• Profit $\Pi$ occurs from maximising revenue after accounting for costs related to production factors.
• Unconditional factor demand is based on maximizing production functions under economic constraints.