Question

The market for lemon has 10 potential consumers, each having an individual demand curve
P = 101 - 10Qi
, where P is price in dollars per cup and Qi is the number of cups demanded
per week by the i
th consumer. Find the market demand curve using algebra. Draw an
individual demand curve and the market demand curve. What is the quantity demanded by
each consumer and in the market as a whole when lemon is priced at P = $1/cup

Answer 1

$Q = \sum_{i=1}^{10}q_i \\ = q_1+q_2+q_3+...+q_{10} \\ = (\frac{101-P}{10})_1 + (\frac{101-P}{10})_2 + (\frac{101-P}{10})_3 + … + (\frac{101-P}{10})_{10} \\ = (10.1 -0.1P)_1 + (10.1 -0.1P)_2 + (10.1 -0.1P)_3 + … + (10.1 -0.1P)_{10} \\ = 10 \times (10.1 -0.1P) \\ = 101 -P \\ P = 101 - Q$

This is the market demand curve for lemonade.

Given the individual demand curve and market demand curve, the graphs will be as follows:

The market demand curve is flatter than the individual demand curve.

Given the price of one cup of lemonade, the individual demand is calculated as follows:

$P = 101 - 10Q_i \\ Q_i = \frac{101-1}{10} = 10$

Hence, the individual demand for lemonade is 10 cups at $1.

The market demand is calculated as follows:

$P = 101 -Q \\ Q = 101 -1 = 100$

Hence, the market demand for lemonade is 100 cups at $1.