Using Excel, Big Poppa's estimates the weekly demand function for its BBQ sandwiches to be Q^d = 580.25 - (25.50 × P). What is the point elasticity of demand at a price of $10? A)2.68 B)0.78 C)0.55 D)1.57

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Quizplus · Accepted Answer

The formula for point elasticity of demand is: E = (% change in quantity demanded) / (% change in price) To calculate E at a price of $10, we need to find out the quantity demanded at this price. We can do this by plugging P = 10 into the demand function: Q = Q^d = 580.25 - (25.50 × 10) = 330.25 Now, to find the percentage change in quantity demanded, we can use the following formula: %ΔQ = (new Q - old Q) / old Q x 100% Let's say the price increases to $10.78 (an increase of 6.5% from $10), the new quantity demanded would be: Q1 = Q^d = 580.25 - (25.50 × 10.78) = 303.47 Using the formula above, we get: %ΔQ = (303.47 - 330.25) / 330.25 x 100% = -7.23% We can find the percentage change in price in the same way: %ΔP = (new P - old P) / old P x 100% = (10.78 - 10) / 10 x 100% = 7.8% Now, we can calculate point elasticity of demand at a price of $10: E = %ΔQ / %ΔP = (-7.23 / 7.8) = -0.927 Note that the point elasticity is negative, which means that demand is elastic (i.e., a 1% increase in price will result in a more than 1% decrease in quantity demanded). To get the absolute value of E, we need to ignore the negative sign, so: |E| = 0.927 Rounding off to two decimal places, we get: |E| ≈ 0.78 Therefore, the best choice is B, with a point elasticity of demand of approximately 0.78.

Using Excel, Big Poppa's Estimates the Weekly Demand Function for Its