Suppose you are a painter, and the price of a gallon of paint increases from $3.00 a gallon to $3.50 a gallon Your usage of paint drops from 35 gallon a month to 20 gallons a month.

Perform the following

Compute the price elasticity of demand for paint and show your calculations.

Decide whether the demand for paint is elastic, unitary elastic, or inelastic.

Explain your reasoning and interpret your results.

To compute the price elasticity of demand for paint, we will use the formula:

Price Elasticity of Demand = Percentage Change in Quantity Demanded / Percentage Change in Price

First, let's calculate the percentage change in quantity demanded:

Percentage Change in Quantity Demanded = (New Quantity Demanded - Old Quantity Demanded) / Old Quantity Demanded

Percentage Change in Quantity Demanded = (20 - 35) / 35
= -15 / 35
= -0.4286 (rounded to four decimal places)

Next, let's calculate the percentage change in price:

Percentage Change in Price = (New Price - Old Price) / Old Price

Percentage Change in Price = ($3.50 - $3.00) / $3.00
= $0.50 / $3.00
= 0.1667 (rounded to four decimal places)

Now, we can calculate the price elasticity of demand:

Price Elasticity of Demand = -0.4286 / 0.1667
= -2.5716 (rounded to four decimal places)

Since the price elasticity of demand is greater than 1, the demand for paint is elastic.

The reasoning behind this is that a change in price (increase from $3.00 to $3.50) resulted in a relatively larger change in quantity demanded (decrease from 35 gallons to 20 gallons). This indicates that the demand is sensitive to price changes, hence elastic.

This interpretation suggests that customers are highly responsive to changes in paint prices. As the price increased, the quantity demanded decreased significantly, indicating that consumers are price-sensitive and may seek alternatives or reduce their consumption when the price of paint rises. Therefore, as a painter, you may need to consider adjusting your pricing strategy or finding ways to minimize costs to maintain sales and profitability.

To calculate the price elasticity of demand, we need to use the following formula:

Price Elasticity of Demand = (% change in quantity demanded) / (% change in price)

First, let's calculate the percentage change in quantity demanded:

% change in quantity demanded = ((new quantity - old quantity) / old quantity) * 100

In this case:
New quantity = 20 gallons
Old quantity = 35 gallons

% change in quantity demanded = ((20 - 35) / 35) * 100 = (-15 / 35) * 100 = -42.86%

Now, let's calculate the percentage change in price:

% change in price = ((new price - old price) / old price) * 100

In this case:
New price = $3.50
Old price = $3.00

% change in price = (($3.50 - $3.00) / $3.00) * 100 = ($0.50 / $3.00) * 100 = 16.67%

Now, substitute the values into the formula:

Price Elasticity of Demand = (-42.86% / 16.67%)

To calculate the exact value of the price elasticity of demand, divide -42.86% by 16.67%:

Price Elasticity of Demand ≈ -2.57

Based on this calculation, the price elasticity of demand for paint is approximately -2.57.

Now let's determine the elasticity of demand:

- If the price elasticity of demand is less than -1, it is considered elastic demand.
- If the price elasticity of demand is equal to -1, it is considered unitary elastic demand.
- If the price elasticity of demand is greater than -1, it is considered inelastic demand.

In this case, the price elasticity of demand (-2.57) is less than -1, indicating that the demand for paint is elastic.

This means that the quantity demanded is highly responsive to price changes. When the price increased by 16.67%, the quantity demanded dropped by 42.86%. This suggests that customers are sensitive to changes in price and will decrease their demand significantly when prices increase.

As a painter, this information is valuable as it shows that price changes will have a significant impact on your paint consumption. It may be beneficial to consider alternative paint options or negotiate with suppliers to maintain profitability. Additionally, understanding the price elasticity of demand can help you make informed decisions about pricing strategies and market positioning.