3. The market for lemon has 10 potential consumers, each having an individual demand

Question

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. 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?
4. The demand for tickets to an Ethiopian Camparada film is given by D(p)= 200,000�

Answer 1

- 5,000p, where D(p) is the quantity demanded in thousands and p is the ticket price in dollars. Find the market demand curve using algebra. Draw the individual demand curve and the market demand curve. What is the quantity demanded by each consumer and in the market as a whole when the ticket price is $10?

To find the market demand curve, we need to sum up the individual demand curves of all consumers.

Given that there are 10 potential consumers, the market demand curve can be calculated as follows:

Qm = Q1 + Q2 + Q3 + ... + Q10

Substituting the values for individual demand curves:

Qm = (101 - 10Q1) + (101 - 10Q2) + (101 - 10Q3) + ... + (101 - 10Q10)

Simplifying further:

Qm = 1010 - 10(Q1 + Q2 + Q3 + ... + Q10)

Now, let's draw the individual demand curve for one consumer:

P = 101 - 10Q

To plot this on a graph, we assign the price P to the y-axis and the quantity Qi to the x-axis. The equation can be rewritten as:

Q = (101 - P)/10

Now, let's plot the market demand curve. The equation for the market demand curve is:

Qm = 1010 - 10(Q1 + Q2 + Q3 + ... + Q10)

Based on the information given, we know that when the price P = $1/cup, we can substitute this value into the individual demand curve equation to find the quantity demanded by each consumer:

Q1 = (101 - 10(1)) = 101 - 10 = 91
Q2 = (101 - 10(1)) = 101 - 10 = 91
Q3 = (101 - 10(1)) = 101 - 10 = 91
...
Q10 = (101 - 10(1)) = 101 - 10 = 91

Therefore, each consumer would demand 91 cups of lemon when priced at $1/cup and the market would demand a total of:

Qm = Q1 + Q2 + Q3 + ... + Q10
Qm = 91 + 91 + 91 + ... + 91 (10 times)
Qm = 910

When the ticket price for the Ethiopian Camparada film is $10, we can substitute this value into the demand equation to find the quantity demanded:

D(p) = 200,000 - 5,000p
D(10) = 200,000 - 5,000(10)
D(10) = 200,000 - 50,000
D(10) = 150,000

Therefore, each consumer would demand 150,000 tickets and the market as a whole would demand a total of 150,000 tickets when priced at $10.