Chapter 4, Problem 7PA

Problems 7 and 8 refer to the demand schedule shown in Table 4P-1. For each price change, say whether demand is elastic, unit-elastic, or inelastic, and say whether total revenue increases, decreases, or stays the same.

Consider each of the following price increase scenarios.

1. Price increases from $10 to $20. Demand is _____ and total revenue _____.
2. Price increases from $30 to $40. Demand is _____ and total revenue _____.
3. Price increases from $50 to $60. Demand is _____ and total revenue _____.

To determine

(a)

To fill: the given blanks with suitable answer.

Answer to Problem 7PA

The demand is "inelastic" and total revenue "increases".

Explanation of Solution

  $\begin{array}{l}\text{Elasticity of demand = }\frac{\Delta Q}{\Delta P}\times \frac{P}{Q}\\ P1=10,P2=20\\ Q1=350,Q2=300\\ \text{Elasticity of demand = }\frac{Q2-Q1}{P2-P1}\times \frac{P1}{Q1}\\ \end{array}$

  $\begin{array}{l}\text{Elasticity of demand = }\frac{300-350}{20-10}\times \frac{10}{350}\\ \text{Elasticity of demand = -0}\text{.14}\end{array}$

Since the negative sign shows the inverse relationship between price and demand,

TR when the price is 10 and the quantity is 350.

  $\begin{array}{l}TR=P\times Q\\ TR=10\times 350\\ TR=3500\end{array}$

TR when the price is 20 and the quantity is 300.

  $\begin{array}{l}TR=P\times Q\\ TR=20\times 300\\ TR=6000\end{array}$

The demand is "inelastic" and total revenue "increases".

To determine

(b)

To fill: the given blanks with suitable answer.

Answer to Problem 7PA

The demand is "inelastic" and total revenue "increases".

Explanation of Solution

  $\begin{array}{l}\text{Elasticity of demand = }\frac{\Delta Q}{\Delta P}\times \frac{P}{Q}\\ P1=30,P2=40\\ Q1=250,Q2=200\\ \text{Elasticity of demand = }\frac{Q2-Q1}{P2-P1}\times \frac{P1}{Q1}\\ \end{array}$

  $\begin{array}{l}\text{Elasticity of demand = }\frac{200-250}{40-30}\times \frac{30}{250}\\ \text{Elasticity of demand = -0}\text{.6}\end{array}$

Since, negative sign shows the inverse relationship between price and demand.

TR when price is 30 and quantity is 250.

  $\begin{array}{l}TR=P\times Q\\ TR=30\times 250\\ TR=7500\end{array}$

TR when price is 40 and quantity is 200.

  $\begin{array}{l}TR=P\times Q\\ TR=40\times 200\\ TR=8000\end{array}$

The demand is "inelastic" and total revenue "increases".

To determine

(c)

To fill: the given blanks with suitable answer.

Answer to Problem 7PA

The demand is "elastic" and total revenue "decrease".

Explanation of Solution

  $\begin{array}{l}\text{Elasticity of demand = }\frac{\Delta Q}{\Delta P}\times \frac{P}{Q}\\ P1=50,P2=60\\ Q1=150,Q2=100\\ \text{Elasticity of demand = }\frac{Q2-Q1}{P2-P1}\times \frac{P1}{Q1}\\ \end{array}$

  $\begin{array}{l}\text{Elasticity of demand = }\frac{100-150}{60-50}\times \frac{50}{150}\\ \text{Elasticity of demand = -1}\text{.67}\end{array}$

Since the negative sign shows the inverse relationship between price and demand. So, it should be ignored.

TR when the price is 50 and the quantity is 150.

  $\begin{array}{l}TR=P\times Q\\ TR=50\times 150\\ TR=7500\end{array}$

TR when the price is 60 and the quantity is 100.

  $\begin{array}{l}TR=P\times Q\\ TR=60\times 100\\ TR=6000\end{array}$

The demand is "elastic" and total revenue "decrease".