Answer to Question #171082 in Microeconomics for segni

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

The individual demand curve is given as follows

P = 101 – 10Q_i

The market demand is the sum total of individuals demand in the market. On taking summation of all 100 individual demand curves, one will get the following:

$$Q = \sum_{i=1}^{10}q_i$$

Q = q₁ + q₂ + q₃ +...+ q₁₀

$Q = [\frac{101 – P}{10}]_1 + [\frac{101 – P}{10}]_2 + [\frac{101 – P}{10}]_3 +...+ [\frac{101 – P}{10}]_{10}$

$Q = (10.1 – 0.1P)_1 + (10.1 – 0.1P)_2 + (10.1 – 0.1P)_3 +...+ (10.1 – 0.1P)_{10}$

On further simplification, the market demand curve is derived as follows

$Q = 10\times ( 10.1 – 0.1P)$

Q = 101 – P

P = 101 – Q

This is 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 more flat than the individual demand curve.

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

P = 101 –10 Q_i

$Q_i = \frac{101 – 1}{10} = 10$

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

The market demand is calculated as follows:

P = 101 – Q

Q = 101 – 1

Q = 100

The market demand for lemonade is 100 cup at $1.