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 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�
- 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.
3. To find the market demand curve, we need to sum up the individual demand curves of all consumers. The individual demand curve is given by P = 101 - 10Qi, where P is the price and Qi is the quantity demanded by the ith consumer.
Let's assume the consumers are labeled from 1 to 10. So, the market demand curve can be found by summing up the individual quantity demanded at each price level.
At a price of P = $1/cup, we can substitute this price into the individual demand equation and calculate the quantity demanded by each consumer.
For consumer 1: P = 101 - 10Q1, where P = $1/cup
1 = 101 - 10Q1
10Q1 = 100
Q1 = 10
Similarly, we can calculate the quantity demanded by the remaining consumers.
For consumer 2: Q2 = 10
For consumer 3: Q3 = 10
...
For consumer 10: Q10 = 10
To find the total quantity demanded in the market, we sum up the individual quantities:
Total Quantity Demanded = Q1 + Q2 + Q3 + ... + Q10
= 10 + 10 + 10 + ... + 10
= 10 * 10
= 100
So, when lemon is priced at P = $1/cup, each consumer will demand 10 cups and the market as a whole will have a total quantity demanded of 100 cups.
Now, let's draw the individual demand curve and the market demand curve.
Individual Demand Curve (for each consumer):
P = 101 - 10Qi
Market Demand Curve:
To find the market demand curve, we need to sum up the individual quantity demanded at each price level. This curve represents the total quantity demanded by all consumers in the market at different prices.
Note: Since we don't have specific price levels, we cannot plot the exact curve. However, it would have a negative slope, indicating that as the price decreases, the quantity demanded increases.
4. The demand function for tickets to an Ethiopian Camparada film is given by D(p) = 200,000 - 30,000p, where D(p) is the quantity demanded and p is the price per ticket.
To find the quantity demanded at a specific price, substitute the given price into the demand equation.
For example, let's find the quantity demanded at p = $10/ticket:
D(p) = 200,000 - 30,000p
D(10) = 200,000 - 30,000 * 10
D(10) = 200,000 - 300,000
D(10) = -100,000
In this case, the quantity demanded at a price of $10/ticket is -100,000. However, since quantity cannot be negative, we can assume that the demand is zero at this price.
Similarly, you can calculate the quantity demanded at different price levels by substituting the specific price into the demand equation.