If the marginal cost of brewing beer is 40 cents and the profit-maximizing price is 90 cents, then the price elasticity of demand is
A)-0.66.
B)-1.8.
C)-2.
D)-2.33.
E)-3.

Question

Quizplus · Accepted Answer

We can use the formula for price elasticity of demand:
E = (% Change in Quantity Demanded) / (% Change in Price)
Since we know that the profit-maximizing price is 90 cents, we can assume that at this price, the quantity demanded is Q1. 
If we were to increase the price by 10% to $0.99, we can assume that the quantity demanded would decrease to Q2. 
Using these values, we can plug them into the formula: 
E = ((Q2-Q1)/((Q1+Q2)/2)) / ((0.99-0.90)/((0.99+0.90)/2)) 
Simplifying this equation, we get:
E = (-(Q2-Q1)/(Q1+Q2)) / (0.09/0.945)
E = -2.1(Q2-Q1)/(Q1+Q2)

We know that the marginal cost of brewing beer is 40 cents, which is less than the profit-maximizing price of 90 cents. This means that the brewery is making a profit at this price. If the price were lower, they would still be making a profit, but it would be less. Therefore, we can assume that the demand for the beer is relatively inelastic, meaning that a change in price will not significantly affect the quantity demanded. This means that Q1 and Q2 will be relatively close to each other. We can assume that a 10% increase in price will lead to a 5% decrease in quantity demanded, so Q2 will be approximately 95% of Q1.

Plugging in these values, we get:
E = -2.1(0.05Q1) / (1.95Q1)
Simplifying this, we get:
E = -0.1077

Rounding to one decimal place, the price elasticity of demand is approximately -0.1, which is equivalent to 0.1 in absolute value. We can then use the answer choices given to see that choice (B) is the closest to 0.1.

If the Marginal Cost of Brewing Beer Is 40 Cents