A craftsman who makes guitars by hand finds that when he prices his guitars at $1 comma 400
,
his annual revenue is $2 comma 800
.
When he prices his guitars at $1 comma 300
,
his annual revenue is $3 comma 900
.
Part 2
Over this range of guitar prices, does the craftsman face elastic, unit-elastic, or inelastic demand?
To determine the elasticity of demand, we can calculate the price elasticity of demand using the formula:
Elasticity = (% change in quantity demanded) / (% change in price).
Let's calculate the percentage change in quantity demanded:
% change in quantity demanded = ((new quantity demanded - original quantity demanded) / original quantity demanded) * 100.
When the price is $1,400, the annual revenue is $2,800, and when the price is $1,300, the annual revenue is $3,900.
% change in quantity demanded = ((3,900 - 2,800) / 2,800) * 100 = 39.29%.
Next, let's calculate the percentage change in price:
% change in price = ((new price - original price) / original price) * 100.
% change in price = ((1,300 - 1,400) / 1,400) * 100 = -7.14%.
Now, let's calculate the price elasticity of demand:
Elasticity = (% change in quantity demanded) / (% change in price) = 39.29% / -7.14%.
The craftsman faces elastic demand as the price elasticity of demand is greater than 1.
To determine whether the craftsman faces elastic, unit-elastic, or inelastic demand, we need to calculate the price elasticity of demand using the given information.
Price elasticity of demand is calculated using the following formula:
E = (Q2 - Q1) / ((Q2 + Q1) / 2) / (P2 - P1) / ((P2 + P1) / 2)
Let's calculate the price elasticity of demand using the given information:
P1 = $1,400
Q1 = $2,800
P2 = $1,300
Q2 = $3,900
E = (3,900 - 2,800) / ((3,900 + 2,800) / 2) / (1,300 - 1,400) / ((1,300 + 1,400) / 2)
E = 1,100 / (6,700 / 2) / (-100) / (2,700 / 2)
E = 1,100 / 3,350 / -100 / 1,350
E = 0.328, which is less than 1
Since the price elasticity of demand is less than 1, it indicates inelastic demand. Inelastic demand means that changes in price have a relatively smaller impact on the quantity demanded.
To determine the elasticity of demand, we need to calculate the percentage change in quantity demanded divided by the percentage change in price. Let's follow these steps:
Step 1: Calculate the percentage change in quantity demanded:
Percentage change in quantity demanded = (New Quantity Demanded - Old Quantity Demanded) / Old Quantity Demanded
When the price is $1,400, the annual revenue is $2,800, so the quantity demanded at this price can be calculated as:
Quantity Demanded at $1,400 = Annual Revenue at $1,400 / Price = $2,800 / $1,400 = 2 guitars
When the price is $1,300, the annual revenue is $3,900, so the quantity demanded at this price can be calculated as:
Quantity Demanded at $1,300 = Annual Revenue at $1,300 / Price = $3,900 / $1,300 = 3 guitars
Using these values, we can calculate the percentage change in quantity demanded:
Percentage change in quantity demanded = (3 - 2) / 2 = 0.5 or 50%
Step 2: Calculate the percentage change in price:
Percentage change in price = (New Price - Old Price) / Old Price = ($1,300 - $1,400) / $1,400 = -0.0714 or -7.14%
Step 3: Calculate the price elasticity of demand:
Price Elasticity of Demand = Percentage change in quantity demanded / Percentage change in price = 50% / -7.14% = -7
Since the price elasticity of demand is -7, we can conclude that the craftsman faces elastic demand over this range of guitar prices. Elastic demand means that a decrease in price leads to a proportionally larger increase in quantity demanded, resulting in higher total revenue.