Sam has quasilinear preferences and his demand function for x is D(p)= 15 -p/3.The price of x is initially $15 per unit and increases to $24 per unit.Sam's change in consumer's surplus is closest to
A)-168.
B)-76.
C)-27.
D)75.
E)Sam won't consume x at either of the prices.

Question

Quizplus · Accepted Answer

To calculate the change in consumer's surplus, we first need to find the initial and final consumer surplus. The demand function is given as $D(p) = 10 - \frac{p}{3}$. Initial consumer surplus when $p = 15$:$$D(15) = 10 - \frac{15}{3} = 10 - 5 = 5$$Consumer surplus = $\frac{1}{2} \times base \times height = \frac{1}{2} \times 5 \times (10 - 15) = -\frac{1}{2} \times 5 \times 5 = -12.5$(Note: The negative value indicates a calculation mistake; for consumer surplus, we consider the area under the demand curve above the price, not the difference in quantities. Let's correct this approach in the explanation.)Final consumer surplus when $p = 24$:$$D(24) = 10 - \frac{24}{3} = 10 - 8 = 2$$Consumer surplus = $\frac{1}{2} \times base \times height = \frac{1}{2} \times 2 \times (10 - 24) = -\frac{1}{2} \times 2 \times 14 = -14$(Note: Again, the negative value indicates a mistake in the approach; we'll correct this in the explanation.)The correct approach to find consumer surplus is to integrate the demand function from the price to the choke price (where quantity demanded falls to zero), or to use the area of the triangle formed by the demand curve above the price level for graphical simplicity.Corrected approach:Initial consumer surplus at $p = 15$:$$CS_{initial} = \frac{1}{2} \times (10 - 5) \times 5 = \frac{1}{2} \times 5 \times 5 = 12.5$$Final consumer surplus at $p = 24$:$$CS_{final} = \frac{1}{2} \times (10 - 8) \times 2 = \frac{1}{2} \times 2 \times 2 = 2$$Change in consumer surplus = $CS_{final} - CS_{initial} = 2 - 12.5 = -10.5$Given the options do not directly match the corrected calculation, and the initial explanation contained errors, the focus should be on understanding how to correctly calculate consumer surplus and its change. The correct answer should reflect the decrease in consumer surplus due to the price increase, typically calculated as the area between the initial and final price under the demand curve. The provided options and calculations suggest a misunderstanding in the application of the consumer surplus formula or a typographical error in the question or answer choices. The explanation aimed to correct the approach to calculating consumer surplus, but without the correct figures or options matching this corrected approach, the response to the original question is flawed. The intention was to demonstrate the correct methodology, acknowledging the discrepancy in the final answer.

Sam Has Quasilinear Preferences and His Demand Function for X