Let's address the first three questions as per the guidelines.
Calculate the price elasticity of demand using the midpoint method for a price change from $20 to $10, with quantity changing from 150 to 350.
Solution:
The midpoint method formula for price elasticity of demand (PED) is:
\[ \text{PED} = \frac{(Q_2 - Q_1)}{(Q_2 + Q_1)/2} \div \frac{(P_2 - P_1)}{(P_2 + P_1)/2} \]
Where:
- \( Q_1 \) and \( Q_2 \) are the initial and final quantities.
- \( P_1 \) and \( P_2 \) are the initial and final prices.
Given:
- \( P_1 = 20 \)
- \( P_2 = 10 \)
- \( Q_1 = 150 \)
- \( Q_2 = 350 \)
First, calculate the percentage change in quantity:
\[ \frac{(Q_2 - Q_1)}{(Q_2 + Q_1)/2} = \frac{(350 - 150)}{(350 + 150)/2} = \frac{200}{250} = 0.8 \]
Next, calculate the percentage change in price:
\[ \frac{(P_2 - P_1)}{(P_2 + P_1)/2} = \frac{(10 - 20)}{(10 + 20)/2} = \frac{-10}{15} = -0.6667 \]
Now, calculate the price elasticity of demand:
\[ \text{PED} = \frac{0.8}{-0.6667} = -1.2 \]
Answer:
The price elasticity of demand is -1.2.
Given demand and supply, calculate equilibrium price and quantity. Introduce a price ceiling of $400 and calculate the resulting shortage.
Solution:
To solve this, we need the demand and supply equations. Let's assume the following linear demand and supply functions for simplicity:
\[ Q_d = 1000 - 2P \]
\[ Q_s = 3P - 200 \]
Step 1: Calculate the equilibrium price and quantity.
At equilibrium, \( Q_d = Q_s \):
\[ 1000 - 2P = 3P - 200 \]
\[ 1000 + 200 = 5P \]
\[ 1200 = 5P \]
\[ P = 240 \]
Now, substitute \( P = 240 \) back into either the demand or supply equation to find the equilibrium quantity:
\[ Q_d = 1000 - 2(240) = 1000 - 480 = 520 \]
Equilibrium Price and Quantity:
- Equilibrium Price: $240
- Equilibrium Quantity: 520 units
Step 2: Introduce a price ceiling of $400 and calculate the resulting shortage.
With a price ceiling of $400, we need to find the quantity demanded and supplied at this price.
\[ Q_d = 1000 - 2(400) = 1000 - 800 = 200 \]
\[ Q_s = 3(400) - 200 = 1200 - 200 = 1000 \]
Resulting Shortage:
\[ \text{Shortage} = Q_d - Q_s = 200 - 1000 = -800 \]
Since the shortage is negative, it indicates a surplus. However, this is counterintuitive given the context of a price ceiling, so let's re-evaluate the demand and supply at the price ceiling:
\[ Q_d = 1000 - 2(400) = 200 \]
\[ Q_s = 3(400) - 200 = 1000 \]
The correct interpretation is that the quantity supplied exceeds the quantity demanded, leading to a surplus of 800 units.
Answer:
- Equilibrium Price: $240
- Equilibrium Quantity: 520 units
- Resulting Surplus (not shortage) with a price ceiling of $400: 800 units
Answered
