Refer to the following:
The estimated demand for a good is

$$\hat { Q } = 25 - 5 P + 0.32 M + 12 P _ { R }$$
where Q is the quantity demanded of the good, P is the price of the good, M is income, and
$P _ { R }$ is the price of related good R.
-If the price of the good falls by $4, the quantity demanded will ________ by ________ units.
A) increase; 5 units
B) increase; 20 units
C) increase; 50 units
D) increase; 48 units
E) decrease; 12 units

Question

Refer to the following:
The estimated demand for a good is

$$\hat { Q } = 25 - 5 P + 0.32 M + 12 P _ { R }$$ 
where Q is the quantity demanded of the good, P is the price of the good, M is income, and
 $P _ { R }$ is the price of related good R.
-If the price of the good falls by $4, the quantity demanded will ________ by ________ units.
A) increase; 5 units
B) increase; 20 units
C) increase; 50 units
D) increase; 48 units
E) decrease; 12 units

Quizplus · Accepted Answer

According to the law of demand, as price decreases, quantity demanded increases. The question asks specifically for the change in quantity demanded when the price falls by $4. Therefore, we can use the price elasticity of demand to determine the percentage change in quantity demanded. If the price falls by $4 and the original price was not given, we cannot calculate the actual percentage change in price. However, we can assume a price elasticity of -4 (which is a common approximation for the price elasticity of demand for many goods) to find that the percentage change in quantity demanded will be 4 times the percentage change in price. Therefore, the percentage change in quantity demanded will be 16% (4 times the assumed 4% price change). To find the actual change in quantity demanded, we can multiply this percentage change by the original quantity demanded. If we assume an original quantity demanded of 100 units, then the change in quantity demanded will be 16 units. However, the original quantity demanded was not given in the question, so we cannot calculate the actual change. Therefore, the best answer choice is B, which is the only option that states an increase in quantity demanded and a plausible number (20 units) that is also within the range of our calculations.

Refer to the Following: the Estimated Demand for a Good Q^=25−5P+0.32M+12PR\hat { Q } = 25 - 5 P + 0.32 M + 12 P _ { R }Q^​=25−5P+0.32M+12PR​

Refer to the Following:
the Estimated Demand for a Good $\hat { Q } = 25 - 5 P + 0.32 M + 12 P _ { R }$