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. For the range from P_X = $60.00 to P_X = $75.00, the arc price elasticity of demand is -3.75.

Question

Quizplus · Accepted Answer

The arc price elasticity of demand is calculated as: (arc elasticity) = [(Q2 - Q1) / (Q2 + Q1) / 2] / [(P2 - P1) / (P2 + P1) / 2] Since the elasticity is given as -3.75, we know that the % change in quantity is 3.75 times the % change in price. Using this information, we can solve for the % change in quantity and % change in price: -3.75 = (% change in quantity) / (% change in price) % change in quantity = -3.75 x % change in price Using the midpoint formula, we can find the average quantity and price for the range: Q1 = Q_X(P1U1B1 = $60) = 1350 Q2 = Q_X(P1U1B1= $75) = 1125 P1 = $60 P2 = $75 Average quantity = (Q1 + Q2) / 2 = 1237.5 Average price = (P1 + P2) / 2 = $67.50 Using the information about P_Y, I, and A, we can plug these values into the demand function to find the quantity demanded at the average price: Qd = 1500 - 100(67.5) + 75(40) + 1.5(2500) + 0.06(5000) = 965 Now we can calculate the % change in quantity and % change in price: % change in quantity = (965 - 1237.5) / ((1237.5 + 965) / 2) = -21.74% % change in price = (75 - 60) / ((60 + 75) / 2) = 20% Plugging in these values to the formula for arc elasticity, we get: -3.75 = (-21.74% / 20%) -3.75 = -1.087 This is not equal, so the statement is false.

Given the Demand Function QX = 1500 - 100PX

Given the Demand Function Q_X = 1500 - 100P_X