Microeconomics Study Guidance: Supply, Demand, and Elasticity in Sports Markets

Q1. If the price of hotdogs rises significantly, explain how and why the market (supply & demand) and equilibrium price and quantity will change for each of the following: ketchup, tomato, tomato juice, and orange juice markets.

Background

Topic: Complements, Substitutes, and Market Equilibrium

This question tests your understanding of how changes in the price of one good (hotdogs) affect related markets (complements and substitutes) through shifts in demand and supply, and how these shifts impact equilibrium price and quantity.

Key Terms and Concepts:

• Complementary Goods: Goods that are often consumed together (e.g., hotdogs and ketchup).

• Substitute Goods: Goods that can replace each other in consumption (e.g., tomato juice and orange juice).

• Market Equilibrium: The point where quantity demanded equals quantity supplied.

• Demand Curve Shift: A change in demand due to factors other than the good's own price.

• Supply Curve Shift: A change in supply due to factors other than the good's own price.

Step-by-Step Guidance

1. Identify the relationship between hotdogs and each market:

   • Ketchup and hotdogs are complements.

   • Tomatoes are an input for ketchup (and possibly for tomato juice).

   • Tomato juice and orange juice may be substitutes.

2. For each market, determine whether the demand or supply curve will shift, and in which direction:

   • If hotdogs become more expensive, consumers buy fewer hotdogs, so demand for complements (like ketchup) decreases (shifts left).

   • Lower demand for ketchup means less demand for tomatoes (input), shifting tomato demand left.

   • Lower tomato prices may affect the supply of tomato juice (input cost falls, supply shifts right).

   • If tomato juice demand falls, consumers may substitute with orange juice, affecting its demand.

3. Draw a supply and demand diagram for each market, indicating the initial equilibrium and the direction of the shift (left for decrease, right for increase).

4. For each market, predict the qualitative effect on equilibrium price and quantity (increase, decrease, or ambiguous) based on the direction of the shift.

Try solving on your own before revealing the answer!

Q2a. Calculate the elasticity of demand for each price interval in the hockey jersey market table.

Background

Topic: Price Elasticity of Demand

This question tests your ability to calculate the price elasticity of demand using the midpoint (arc elasticity) formula for each price interval in a demand schedule.

Key Terms and Formulas:

• Price Elasticity of Demand ($E_d$): Measures the responsiveness of quantity demanded to a change in price.

$E_d = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}}$

Midpoint (arc elasticity) formula:

$E_d = \frac{\frac{Q_2 - Q_1}{(Q_1 + Q_2)/2}}{\frac{P_2 - P_1}{(P_1 + P_2)/2}}$

Step-by-Step Guidance

1. For each price interval, identify $P_1$, $P_2$, $Q_1$, and $Q_2$ from the table.

2. Calculate the percentage change in quantity demanded using the midpoint formula:

   $\%\ \text{change in Q} = \frac{Q_2 - Q_1}{(Q_1 + Q_2)/2}$

3. Calculate the percentage change in price using the midpoint formula:

   $\%\ \text{change in P} = \frac{P_2 - P_1}{(P_1 + P_2)/2}$

4. Divide the percentage change in quantity by the percentage change in price to get the elasticity for each interval.

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Q2b. Using a properly labelled graph, illustrate the market for jerseys given the cost to manufacture each jersey is $50.

Background

Topic: Supply and Demand Graphing

This question tests your ability to graphically represent the market for a good, including the demand curve, supply curve (based on cost), and equilibrium points.

Key Terms and Concepts:

• Demand Curve: Shows the relationship between price and quantity demanded.

• Supply Curve: Shows the relationship between price and quantity supplied; here, supply is perfectly elastic at $50 (the cost).

• Equilibrium: Where supply and demand intersect.

Step-by-Step Guidance

1. Plot the demand points from the table on a graph with price on the vertical axis and quantity on the horizontal axis.

2. Draw the demand curve by connecting the plotted points.

3. Draw the supply curve as a horizontal line at $P = 50$, since the cost to manufacture is constant at $50$ per jersey.

4. Label the axes, curves, and equilibrium points clearly.

Try sketching the graph before revealing the answer!

Q2c. At a price of $300, calculate the current revenue and quantity of jerseys sold. Show this on your graph.

Background

Topic: Revenue Calculation and Graphical Representation

This question tests your ability to calculate total revenue and identify the corresponding quantity sold at a given price, and to represent this on a supply and demand graph.

Key Terms and Formulas:

• Total Revenue (TR): The total amount received from sales, calculated as $TR = P \times Q$.

Step-by-Step Guidance

1. From the demand table, find the quantity sold at $P = 300$.

2. Calculate total revenue using the formula:

   $TR = P \times Q$

3. On your graph, mark the point where $P = 300$ and the corresponding quantity sold.

Try calculating before revealing the answer!

Q2d. Based on your elasticity calculations, should the team raise or lower the price of their jerseys? Explain.

Background

Topic: Elasticity and Revenue Maximization

This question tests your understanding of how price elasticity of demand affects total revenue and optimal pricing decisions.

Key Terms and Concepts:

• Inelastic Demand: $|E_d| < 1$; total revenue moves in the direction of price change.

• Elastic Demand: $|E_d| > 1$; total revenue moves opposite to price change.

Step-by-Step Guidance

1. Review your elasticity calculations for the relevant price interval ($P = 300$).

2. Determine if demand is elastic or inelastic at this price point.

3. Recall the rule: If demand is inelastic, raising price increases total revenue; if elastic, lowering price increases total revenue.

4. Apply this rule to decide whether the team should raise or lower the price, and explain your reasoning.

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Q2e. Suppose 25% of jerseys sold have the name and number of the top player. Show his demand curve on your graph.

Background

Topic: Market Segmentation and Demand Curves

This question tests your ability to interpret and graph a segment of the market demand curve for a specific product variant (player-specific jerseys).

Key Terms and Concepts:

• Market Segmentation: Dividing the market into groups based on product characteristics.

• Demand Curve for a Segment: The demand for a subset of the total market (e.g., jerseys for a specific player).

Step-by-Step Guidance

1. From the total quantity sold at each price, calculate 25% to estimate the quantity for the top player's jerseys.

2. Plot these points on the same graph as the overall demand curve, labeling this new curve (e.g., D1).

3. Compare the position of this curve to the overall demand curve (it should be lower and parallel).

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Q2f. After the top player is traded, explain why his jersey is now sold for $100.

Background

Topic: Shifts in Demand Due to Changes in Preferences

This question tests your understanding of how changes in consumer preferences (e.g., a player being traded) affect demand and market price.

Key Terms and Concepts:

• Demand Shift: A change in demand due to external factors (e.g., player leaves team).

• Clearance Pricing: Lowering price to sell remaining inventory when demand falls.

Step-by-Step Guidance

1. Explain how the player's trade reduces demand for his jersey (leftward shift in demand curve).

2. Discuss how a lower demand leads to a lower equilibrium price, possibly below cost, to clear inventory.

3. Relate this to the observed price drop to $100 for the jersey.

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