Answer to Question #276551 in Microeconomics for theo

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 ith consumer.

A. Find the market demand curve using algebra.

B. Draw an individual demand curve and the market demand curve

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.