Given the demand function Q_X = 1500 - 100P_X + 75P_Y + 1.5I + .06A where P_Y = $40.00, I = $2500, and A = $5,000. When price of good X is increased from $60.00 to $75.00, we know that demand for good X over this range is:

Question

Quizplus · Accepted Answer

To determine the elasticity of demand, we need to calculate the percentage change in the quantity demanded of good X divided by the percentage change in its price.

Using the midpoint method, we have:

- Initial price (P1) = $60.00
- New price (P2) = $75.00
- Average price = (P1+P2)/2 = ($60.00+$75.00)/2 = $67.50
- Quantity demanded at P1 (Q1) = 1500 - 100(60) + 75(40) + 1.5(2500) + 0.06(5000) = 1500 - 6000 + 3000 + 3750 + 300 = 8550
- Quantity demanded at P2 (Q2) = 1500 - 100(75) + 75(40) + 1.5(2500) + 0.06(5000) = 1500 - 7500 + 3000 + 3750 + 300 = 8550

The percentage change in price is [(75-60)/67.5] x 100% = 22.22%.

The percentage change in quantity demanded is [(8550-8550)/8550] x 100% = 0%.

The price elasticity of demand (PED) is therefore 0%/22.22% = 0, which means demand for good X is perfectly inelastic over this price range. However, since none of the answer choices include "perfectly inelastic," the closest answer is A) elastic. This is because elasticity is determined by the absolute value of PED, and 0 is less than 1 in absolute value, which is the threshold for elasticity.

Given the Demand Function QX = 1500 - 100PX

Given the Demand Function Q_X = 1500 - 100P_X