Final answer:
The market demand curve can be obtained by adding the individual demand curves of Mary, Jack, and Helen. The market demand curve is QD = 8000 – 12P.
Step-by-step explanation:
The market demand curve can be obtained by adding the individual demand curves of Mary, Jack, and Helen. Given:
Mary’s demand curve: 5P = 5000 – 1.25QM
Jack’s demand curve: P = 1000 – 0.5QJ
Helen’s demand curve: QH = 2000 – 2P
To obtain the market demand curve, we need to sum the values of QM, QJ, and QH. However, since the equations are given in terms of P and Q, we need to convert them into the same variables. Let's solve each equation for Q, resulting in:
Mary’s demand equation: QM = 4000 – 8P
Jack’s demand equation: QJ = 2000 – 2P
Helen’s demand equation: QH = 2000 – 2P
Now, we can sum the three demand equations to obtain the market demand equation:
QD = QM + QJ + QH = (4000 – 8P) + (2000 – 2P) + (2000 – 2P)
QD = 8000 – 12P
So, the market demand curve is QD = 8000 – 12P.