In which of the following cases will a firm's total revenue increase when there is a change in price?

Introduction / Context:
Total revenue is the product of price and quantity demanded. The effect of a price change on total revenue depends on the price elasticity of demand, which measures how responsive quantity demanded is to price changes. This question tests your understanding of the relationship between price elasticity and total revenue by asking in which situation total revenue increases when price changes.

Given Data / Assumptions:

• Total revenue (TR) is defined as price multiplied by quantity demanded.
• Elastic demand means that the absolute value of elasticity is greater than one.
• Inelastic demand means that the absolute value of elasticity is less than one.
• The question focuses on the demand side; supply elasticity mentioned in one option is a distraction.

Concept / Approach:
For inelastic demand, a percentage change in price is larger than the percentage change in quantity demanded. When price rises, the drop in quantity is proportionately smaller, so total revenue rises. When price falls under inelastic demand, total revenue falls. Under elastic demand, the opposite holds: an increase in price reduces total revenue, while a decrease in price increases it. Therefore, the correct option is the one where price rises and demand is inelastic, because that is when total revenue increases.

Step-by-Step Solution:
Step 1: Recall the rule that if demand is inelastic, price and total revenue move in the same direction. Step 2: Recall that if demand is elastic, price and total revenue move in opposite directions. Step 3: Examine option A, where price rises and demand is inelastic. Here, total revenue should increase. Step 4: Examine option C, where price rises and demand is elastic. In this case, total revenue would decrease, not increase. Step 5: Examine option D, where price falls and demand is inelastic. Here, total revenue would also decrease, so option A is the only one that leads to higher total revenue.

Verification / Alternative check:
Consider a numerical example. Suppose the price of a good is 10 and quantity demanded is 100, so total revenue is 1000. Assume demand is inelastic such that a 10 percent increase in price causes only a 5 percent drop in quantity. If price rises to 11, quantity falls to 95. Total revenue becomes 11 multiplied by 95, which is 1045, greater than the original 1000. This shows that with inelastic demand, a price increase leads to higher total revenue, which matches option A.

Why Other Options Are Wrong:
Option B is wrong because it focuses on supply elasticity, which does not directly determine the effect of price changes on total revenue from the demand side. Option C is wrong because with elastic demand, a price rise causes a proportionally larger fall in quantity, reducing total revenue. Option D is wrong because when demand is inelastic, a price fall leads to a smaller proportional increase in quantity, causing total revenue to decline.

Common Pitfalls:
Students often mix up the inelastic and elastic cases or ignore which side of the market is being discussed. Another error is to think that total revenue always moves in the same direction as price, regardless of elasticity. A helpful rule is to draw a small table of cases for elastic and inelastic demand and check how price changes affect revenue. Remember that with inelastic demand, price and total revenue move together, while with elastic demand, they move in opposite directions.

Final Answer:
Total revenue will increase in the case where price rises and demand is inelastic, which corresponds to option A.