L12 Revenue and Profit Max

Principles of Microeconomics

Topic 3: Producer Theory

• Lecture 12: Profit Maximisation

• Instructor: Tien-Der Jerry Han

Aims of the Lecture

• Focus on Profit Maximisation:

  • Examination of firm's production outputs and revenue.

  • Review of production and costs from the last lecture.

  • Assessment of potential revenue and profit levels.

  • Key questions:

    • How much revenue can a firm earn at a set price?

    • What output level is sufficient to warrant production?

  • Linkage to previous topics.

  • Main goal: Deriving the firm's supply curve.

Lecture Outline

1. Various Measures of Revenue

2. Shut Down Rule: Criteria for when a firm should cease production.

3. Marginal Output Rule: Determining profit maximisation points.

Reading Materials

• Lipsey and Chrystal (14ed), Chapter 6, pp. 134-140

• Lipsey and Chrystal (13ed), Chapter 6, pp. 129-134

• Sloman, Wride and Garratt (11ed), Chapter 5, pp. 185-186

• Sloman, Wride and Garratt (9ed), Chapter 5.6, pp. 162-163

Price Takers vs. Price Makers

Price Takers

• Characteristics:

  • Can sell any quantity at a fixed market price.

  • Small market size relative to overall market.

• Price Elasticity of Demand (PED) formula:

  • % Change in Price = - % Change in Quantity Demanded/PED

Price Makers

• Characteristics:

  • Market price is affected by the quantity sold.

  • Buyers affect market price based on quantity purchased.

Revenue, Costs, and Profit for Price Takers

• Normal Profit: Firm breaks even when producing at outputs q’ or q’’.

• Supernormal Profit: Total revenue exceeds costs.

• Economic Profit:

  • Economic profit = 0 at q’ and q’’.

  • Economic profit > 0 indicates profitability.

Various Measures of Revenue

Average Revenue (AR)

• Formula:

  • AR = Total Revenue (TR) / Quantity Sold (Q)

  • Practical Example: Selling 100 units at £5 yields:

    • TR = £5 x 100 = £500

    • AR = £500 / 100 = £5

Marginal Revenue (MR)

• Definition: The additional revenue generated from selling one more unit of output.

• Formula:

  • MR = ∆TR / ∆Q = TR(Q+1) – TR(Q)

Relationship Between AR and MR for Price Takers

• Market Price: £10, thus:

  • AR = MR = 10 for all output levels.

• Demonstrated stability in revenue with constant pricing.

The Shut Down Rule: Production Decisions

• Profit Equation:

  • Profit (π) = Total Revenue (TR) - Total Fixed Costs (TFC) - Total Variable Costs (TVC)

• In the Short-Run:

  • Shut down if price (p) < Average Variable Cost (AVC).

  • Can cover some fixed costs if TR > TVC.

• In the Long-Run:

  • All costs are variable: p < Long-Run Average Cost (LRAC) indicates shutdown.

Example of Shut Down Rule

• If fixed costs remain at £12, a firm incurs losses with insufficient revenue, resulting in decisions to adjust output or cease operations.

Marginal Output Rule: Output Production Levels

• Optimal production occurs where:

  • Marginal Revenue (MR) = Marginal Cost (MC)

• Explanation:

  • If MR > MC, increasing output enhances profits (π = TR - TC).

Summary of Key Concepts

• Price Takers: No influence on market prices.

• Short-Run Shut Down Rule: p < AVC.

• Long-Run Shut Down Rule: p < LRAC.

• Marginal Output Rule: Maximisation at MR = MC.

Learning Outcomes

• Explain shapes of total, average, and marginal revenue for price-taking firms.

• Determine optimal output for profit maximisation and assess shutdown criteria in the short run.

• Illustrate shut down and marginal output rules visually.