Question

The price elasticity of demand for beer has been estimated to be about-05. Data from the Beer Institute for 2017 shows that Louisiana beer drinkers consumed 144 million gallons of beer that year. In 2017, the average retail price per gallon of beer about $48.00. Using this information, derive the linear demand function for the beer market in Louisiana in 2017.

Answer 1

The linear demand function for the beer market in Louisiana in 2017 can be expressed as: Quantity demanded = 151.2 million - 0.5 * Price

Step-by-step explanation:

The price elasticity of demand for beer can be calculated using the formula:

Elasticity = Percentage change in quantity demanded / Percentage change in price

Given that the price elasticity of demand for beer is -0.5, we can use the formula to calculate the percentage change in quantity demanded:

-0.5 = Percentage change in quantity demanded / Percentage change in price

Let's assume that the percentage change in price is a 10% decrease, so the percentage change in price would be -10%:

-0.5 = Percentage change in quantity demanded / -10%

Now, solve for the percentage change in quantity demanded:

Percentage change in quantity demanded = -0.5 * -10% = 5%

Since we know that Louisiana beer drinkers consumed 144 million gallons of beer in 2017 and the average retail price per gallon was $48.00, we can use the percentage change in quantity demanded to calculate the new quantity demanded:

New quantity demanded = 144 million gallons * (1 + 5%) = 151.2 million gallons

Therefore, the linear demand function for the beer market in Louisiana in 2017 can be expressed as:

Quantity demanded = 151.2 million - 0.5 * Price