The quantity demanded (in units of a hundred) of the miniature cameras per week is related to the unit price (in dollars) by and the quantity (in units of a hundred) that the supplier is willing to make available in the market is related to the unit price (in dollars) by If the market price is set at the equilibrium price, find the consumers' surplus and the producers' surplus.Please round the answers to the nearest dollar.
A)The consumers' surplus: $26,704, the producers' surplus: $142,718
B)The consumers' surplus: $142,718, the producers' surplus: $26,704
C)The consumers' surplus: $18,333, the producers' surplus: $20,000
D)The consumers' surplus: $20,000, the producers' surplus: $18,333
E)The consumers' surplus: $44,040, the producers' surplus: $21,478

Question

The quantity demanded  (in units of a hundred) of the miniature cameras per week is related to the unit price  (in dollars) by  and the quantity  (in units of a hundred) that the supplier is willing to make available in the market is related to the unit price  (in dollars) by  If the market price is set at the equilibrium price, find the consumers' surplus and the producers' surplus.Please round the answers to the nearest dollar.
A)The consumers' surplus: $26,704, the producers' surplus: $142,718 
B)The consumers' surplus: $142,718, the producers' surplus: $26,704 
C)The consumers' surplus: $18,333, the producers' surplus: $20,000 
D)The consumers' surplus: $20,000, the producers' surplus: $18,333 
E)The consumers' surplus: $44,040, the producers' surplus: $21,478

Quizplus · Accepted Answer

To find the equilibrium price, we need to equate the quantity demanded and the quantity supplied:
190 - 10P = 50P - 120
60P = 310
P = 5.17
The equilibrium quantity can be found by substituting the equilibrium price into either the demand or supply function:
Q = 190 - 10(5.17) = 136.3 (rounded to 136)
The consumers' surplus is the area below the demand curve and above the equilibrium price, while the producers' surplus is the area above the supply curve and below the equilibrium price. To calculate the consumers' surplus, we need to integrate the demand curve from zero to the equilibrium quantity and subtract the area of the triangle formed by the equilibrium quantity, the equilibrium price, and the quantity axis. Similarly, to calculate the producers' surplus, we need to integrate the supply curve from zero to the equilibrium quantity and add the area of the triangle formed by the equilibrium quantity, the equilibrium price, and the quantity axis. Using the provided equations, we can derive the demand and supply curves:
Q = 190 - 10P
Q/100 = 1.9 - 0.1P
P = 0.02Q + 4.76
Q = 50P - 120
Q/100 = 0.5P - 1.2
P = 2Q/5 + 2.4
Integrating the demand curve from zero to 136 and subtracting the area of the triangle, we get:
CS = 1/2 * (5.17 - 0) * (190 - 5.17*10) - ∫(1.9 - 0.1P) dQ from 0 to 136
CS = 961.65 - [1/2 * (136/100 - 0/100) * (0.02*136 + 4.76 + 1.9*0 - 1.9*136/100)]
CS = 961.65 - 733.35
CS = 228.3 (rounded to 228)
Integrating the supply curve from zero to 136 and adding the area of the triangle, we get:
PS = ∫(0.5P - 1.2) dQ from 0 to 136 + 1/2 * (136/100 - 0/100) * (0.02*136 + 4.76 - 1.2*136/100 - 1.9*0)
PS = [1/4 * (136/100)^2 - 1.2*136/100] + 438.14
PS = 363.86 (rounded to 364)
Therefore, the consumers' surplus is $228 and the producers' surplus is $364, rounded to the nearest dollar. The best choice is D.

The Quantity Demanded (In Units of a Hundred) of the Miniature