Answer to Question #214588 in Microeconomics for Dani 122112

Question

3. 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 ithconsumer. Find the market demand curve using algebra. 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

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

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.