📖 Chapter 2: Price Elasticity of Demand and Revenue

What this chapter covers: This chapter explores the relationship between price elasticity of demand (PED) and a firm's revenue. It defines PED and explains how it affects total revenue when prices change. The chapter then relates elasticity of demand to the revenue curves, particularly in price-taking and price-searching markets. Understanding this relationship is crucial for firms to make informed pricing decisions.

🔑 Essential Concepts & Formulas

🛠️ Problem Types

Type A: Calculating PED and Predicting Revenue Changes

Setup: "Given percentage changes in price and quantity demanded, or information to calculate them."

Method: "Calculate PED using the formula. If demand is elastic, a price increase will decrease total revenue, and vice versa. If demand is inelastic, a price increase will increase total revenue, and vice versa."

Example: "If the price of a product increases by 5% and the quantity demanded decreases by 10%, calculate PED and predict the impact on total revenue."

Type B: Relating Elasticity of Demand to Revenue Curves

Setup: "Analyzing the shape of the MR curve to determine the elasticity of demand."

Method: "When MR is positive, demand is elastic; when MR is negative, demand is inelastic; and when MR is zero, demand is unitarily elastic."

Example: "Draw the MR curve and indicate the regions where demand is elastic, inelastic, and unitarily elastic."

🧮 Solved Example

Problem: The price of a product increases by 2%, and the quantity demanded decreases by 4%. Calculate the price elasticity of demand and determine whether demand is elastic or inelastic. Predict the impact on total revenue.

Given:

• $\% \Delta P = 2\%$
• $\% \Delta Q = -4\%$

Steps:

1. Calculate $PED = \frac{\% \Delta Q}{\% \Delta P} = \frac{-4\%}{2\%} = -2$
2. Since $|PED| = 2 > 1$, demand is elastic.
3. Since demand is elastic, a price increase will decrease total revenue.

"

✅

Answer: $PED = -2$, Demand is elastic, Total revenue will decrease.

⚠️ Common Mistakes

❌ Mistake 1: Forgetting the negative sign in the PED calculation.

✅ How to avoid: Always include the negative sign to indicate the inverse relationship between price and quantity demanded.

❌ Mistake 2: Incorrectly interpreting the impact of PED on revenue.

✅ How to avoid: Remember that elastic demand means a price increase decreases revenue, and inelastic demand means a price increase increases revenue.

🦁 Erik's Tip

Think of PED as a seesaw. If price goes up and quantity goes down a lot (elastic), revenue goes down. If price goes up and quantity barely changes (inelastic), revenue goes up.

📖 Chapter 3: Cost Concepts in Short Run and Long Run

What this chapter covers: This chapter introduces the fundamental concepts of cost, differentiating between fixed and variable costs in the short and long run. It covers the mathematical calculation of various costs, including total cost (TC), average cost (AC), and marginal cost (MC). The chapter provides a foundation for understanding how costs behave in different production scenarios.

🔑 Essential Concepts & Formulas

🛠️ Problem Types

Type A: Differentiating Between Fixed and Variable Costs

Setup: "Given a list of costs, identify which are fixed and which are variable."

Method: "Fixed costs do not change with output, while variable costs do."

Example: "Classify the following costs as fixed or variable: rent, raw materials, wages, advertising."

Type B: Calculating TC, AC, and MC

Setup: "Given cost and output data, calculate total cost, average cost, and marginal cost."

Method: "Apply the formulas $TC = TFC + TVC$, $AC = \frac{TC}{Q}$, and $MC = \frac{\Delta TC}{\Delta Q}$."

Example: "A firm has fixed costs of $100 and variable costs of$200 when producing 10 units. If they produce 11 units, total cost increases to $310. Calculate TC, AC, and MC for both scenarios."

Type C: Analyzing the Law of Diminishing Returns

Setup: "Given data on inputs and outputs, determine if the law of diminishing returns is present."

Method: "As more of a variable factor is added to a fixed factor, the marginal product of the variable factor will eventually decrease."

Example: "A farmer adds fertilizer to a field. Initially, the yield increases significantly, but after a certain point, the increase in yield becomes smaller and smaller. Explain this phenomenon."

🧮 Solved Example

Problem: A firm has fixed costs of $500. Variable costs are$1000 when producing 20 units and $1600 when producing 30 units. Calculate the total cost, average cost, and marginal cost for both production levels.

Given:

• $TFC =$500$
• $TVC_1 =$1000, Q_1 = 20$
• $TVC_2 =$1600, Q_2 = 30$

Steps:

1. Calculate $TC_1 = TFC + TVC_1 =$500 + $1000 =$1500$
2. Calculate $TC_2 = TFC + TVC_2 =$500 + $1600 =$2100$
3. Calculate AC_1 = \frac{TC_1}{Q_1} = \frac{1500}{20} = $75$
4. Calculate AC_2 = \frac{TC_2}{Q_2} = \frac{2100}{30} = $70$
5. Calculate $\Delta TC = TC_2 - TC_1 =$2100 - $1500 =$600$
6. Calculate $\Delta Q = Q_2 - Q_1 = 30 - 20 = 10$
7. Calculate MC = \frac{\Delta TC}{\Delta Q} = \frac{600}{10} = $60$

"

✅

Answer: $TC_1 =$1500$,$AC_1 = $75$, $TC_2 =$2100$,$AC_2 = $70$, $MC =$60$

⚠️ Common Mistakes

❌ Mistake 1: Confusing fixed and variable costs.

✅ How to avoid: Remember that fixed costs do not change with output, while variable costs do.

❌ Mistake 2: Incorrectly calculating MC by not accounting for the change in output.

✅ How to avoid: Use the formula $MC = \frac{\Delta TC}{\Delta Q}$ and ensure you calculate the change in total cost and output correctly.

🦁 Erik's Tip

Visualize the cost curves. Understanding the U-shape of the AC and MC curves due to the law of diminishing returns is crucial.