Find the consumer and producer surpluses by using the demand and supply functions, where p is the price (in dollars) and x is the number of units (in millions). Demand Function$~~~~~~~~~~~~~~~~$ Supply Function
$P = 975 - 23 x ~~~~~~~~~~~\quad 42 x$
A)a. $2587.50b. $3725.00
B)a. $5587.50b. $4725.00
C)a. $2587.50b. $1725.00
D)a. $1587.50b. $4725.00
E)a. $3587.50b. $4725.00

Question

Quizplus · Accepted Answer

To find the consumer and producer surpluses, we first need to find the equilibrium price and quantity where the demand equals the supply. Setting the demand and supply functions equal to each other:$975 - 23x = 42x$Solving for $x$, we get:$975 = 65x$$x = 15$So, the equilibrium quantity is 15 million units. To find the equilibrium price ($P$), we can substitute $x$ back into either the demand or supply function:$P = 975 - 23(15) = 630$Now, to find the consumer surplus, we calculate the area of the triangle formed by the demand curve above the price level up to the intercept:Consumer Surplus = $0.5 \times (975 - 630) \times 15 = 0.5 \times 345 \times 15 = 2587.50$For the producer surplus, we calculate the area of the triangle below the price level down to the x-axis:Producer Surplus = $0.5 \times 630 \times 15 = 4725.00$However, there seems to be a mistake in the calculation or the options provided for the producer surplus as per the given method and options. Based on the correct approach, the producer surplus calculation provided does not match the expected outcome from the given method. The correct producer surplus should be calculated as follows:Producer Surplus = $0.5 \times (630 - 0) \times 15 = 0.5 \times 630 \times 15 = 4725.00$Given the discrepancy and focusing on the correct approach to calculate the consumer and producer surpluses, the correct answer based on the initial calculation method for consumer surplus is:Consumer Surplus = $2587.50However, the options for producer surplus in the context of the calculation provided seem to be inconsistent with the standard approach. Therefore, based on the provided options and recognizing a potential error in the interpretation or the options themselves, the closest match to the expected method of calculation is:C) a. $2587.50 b. $1725.00This answer is selected based on the correct calculation for consumer surplus and acknowledging a potential error or misunderstanding in the calculation or presentation of producer surplus options.

Find the Consumer and Producer Surpluses by Using the Demand ~~~~~~~~~~~~~~~~

Find the Consumer and Producer Surpluses by Using the Demand $~~~~~~~~~~~~~~~~$