Answer to Question #135853 in Economics of Enterprise for Hadgu

Question

7. The market for lemon has 100 potential consumers, each having an individual demand curve: P = 201 - 100Qi, where P is price in dollars per cup and Qi is the number of cups demanded per week by the ith 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 = 201 – 100Q_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:

$$Q = \sum_{i=1}^{100}q_i$$

Q = q₁ + q₂ + q₃ +...+ q₁₀₀

$Q = [\frac{201 – P}{100}]_1 + [\frac{201 – P}{100}]_2 + [\frac{201 – P}{100}]_3 +...+ [\frac{201 – P}{100}]_{100}$

$Q = (2.01 – 0.01P)_1 + (2.01 – 0.01P)_2 + (2.01 – 0.01P)_3 +...+ (2.01 – 0.01P)_{100}$

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

$Q = 100\times ( 2.01 – 0.01P)$

Q = 201 – P

P = 201 – 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 = 201 – Q_i

$Q_i = \frac{201 – 1}{100} = 2$

Hence, the individual demand for lemonade is 2 cup at $1.

The market demand is calculated as follows:

P = 201 – Q

Q = 201 – 1

Q = 200

The market demand for lemonade is 200 cup at $1.