Question

question 5
when demand is price inelastic, ceteris paribus:
○ an increase in price leads to lower total revenue.
○ an increase in total revenue means quantity rises.
○ an increase in total revenue indicates a reduction in price.
○ an increase in price leads to greater total revenue.

question 6
for a certain good, when price rises from $90 to $98, quantity demanded falls from 90,000 to 86,000. the price elasticity of demand here is
○ 0.65.
○ 1.87.
○ 0.796.
○ 0.53.

Explanation:

Question 5

To solve this, we recall the concept of price - inelastic demand. Price - inelastic demand means that the percentage change in quantity demanded is less than the percentage change in price (\(E_d< 1\)). Total revenue (\(TR\)) is calculated as \(TR = P\times Q\). When demand is inelastic and price (\(P\)) increases, the percentage decrease in quantity demanded (\(Q\)) is smaller than the percentage increase in price. So, \(TR=P\times Q\) will increase because the increase in \(P\) has a larger impact than the decrease in \(Q\).

Let's analyze each option:

• Option 1: An increase in price leads to lower total revenue. This is incorrect. For inelastic demand, an increase in price leads to an increase in total revenue.
• Option 2: An increase in total revenue means quantity rises. This is incorrect. For inelastic demand, if total revenue increases, it is because price has increased (and quantity has decreased, but the percentage change in price is larger).
• Option 3: An increase in total revenue indicates a reduction in price. This is incorrect. A reduction in price for inelastic demand would lead to a decrease in total revenue.
• Option 4: An increase in price leads to greater total revenue. This is correct as explained by the concept of price - inelastic demand.

Step 1: Recall the formula for price elasticity of demand (\(E_d\))

The formula for price elasticity of demand is \(E_d=\frac{\%\Delta Q}{\%\Delta P}\), where \(\%\Delta Q=\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}\times100\) and \(\%\Delta P=\frac{P_2 - P_1}{(P_2 + P_1)/2}\times100\)

Step 2: Calculate \(\%\Delta Q\)

Given \(Q_1 = 90000\), \(Q_2=86000\)
\(\%\Delta Q=\frac{86000 - 90000}{(86000 + 90000)/2}\times100=\frac{- 4000}{88000}\times100\approx - 4.545\%\)

Step 3: Calculate \(\%\Delta P\)

Given \(P_1 = 90\), \(P_2 = 98\)
\(\%\Delta P=\frac{98 - 90}{(98+90)/2}\times100=\frac{8}{94}\times100\approx8.511\%\)

Step 4: Calculate \(E_d\)

\(E_d=\frac{\vert\%\Delta Q\vert}{\%\Delta P}=\frac{4.545\%}{8.511\%}\approx0.53\) (we take the absolute value because elasticity is usually reported as a positive number for the magnitude)

Answer:

D. An increase in price leads to greater total revenue.

Question 6