Final answer:
The market equilibrium quantity is found by setting QD equal to QS and solving for P. The approximate P value is then used to calculate QS, which comes out to approximately 76.4, a value not included in the provided answer choices. This suggests there may be an error with the question or the answer options.
Step-by-step explanation:
To determine the market equilibrium quantity, we need to set the quantity demanded (QD) equal to the quantity supplied (QS), and solve for the price (P) that equates both. The student has provided demand and supply equations as:
- QD = -55.3P + 114.5
- QS = 56.5P + 37.5
At equilibrium, we set QD equal to QS:
-55.3P + 114.5 = 56.5P + 37.5
Solving for P, we combine like terms:
-55.3P - 56.5P = 37.5 - 114.5
-111.8P = -77
P = 77 / 111.8
P = 0.688 approximately
Substituting this value back into either the demand or supply equation, we choose the supply equation for ease:
QS = 56.5(0.688) + 37.5
QS = 38.872 + 37.5
QS = 76.372
Therefore, the market equilibrium quantity is approximately 76.4, which is not an option provided. There seems to be a misunderstanding with the question or the answer choices given.