To calculate the market demand, we need to sum up the individual demand functions for each type of consumer.
For the first type of consumer with demand 𝑄𝑑 = 10 − 2𝑝, let's denote the number of consumers of this type as 𝑛1. Therefore, their total demand is 𝑛1(10 - 2𝑝).
For the second type of consumer with demand 𝑄𝑑 = 10 − 5𝑝, let's denote the number of consumers of this type as 𝑛2. Therefore, their total demand is 𝑛2(10 - 5𝑝).
Now, let's consider the three cases:
Case 1: 𝑛1 = 1 and 𝑛2 = 1
The market demand in this case is 𝑛1(10 - 2𝑝) + 𝑛2(10 - 5𝑝) = 1(10 - 2𝑝) + 1(10 - 5𝑝) = 20 - 2𝑝 + 10 - 5𝑝 = 30 - 7𝑝.
Case 2: 𝑛1 = 2 and 𝑛2 = 1
The market demand in this case is 𝑛1(10 - 2𝑝) + 𝑛2(10 - 5𝑝) = 2(10 - 2𝑝) + 1(10 - 5𝑝) = 20 - 4𝑝 + 10 - 5𝑝 = 30 - 9𝑝.
Case 3: 𝑛1 = 1 and 𝑛2 = 2
The market demand in this case is 𝑛1(10 - 2𝑝) + 𝑛2(10 - 5𝑝) = 1(10 - 2𝑝) + 2(10 - 5𝑝) = 20 - 2𝑝 + 20 - 10𝑝 = 40 - 12𝑝.
Now, let's sketch the market demand function for each case:
Case 1: Market Demand = 30 - 7𝑝
This is a linear function with a negative slope of -7.
Case 2: Market Demand = 30 - 9𝑝
This is also a linear function with a negative slope of -9.
Case 3: Market Demand = 40 - 12𝑝
This is a linear function with a negative slope of -12.
To sketch these functions, we can use a graph with 𝑝 (price) on the x-axis and 𝑄𝑑 (quantity demanded) on the y-axis. The slope of the line represents the coefficient of 𝑝 in the demand function.
Here is a visual representation of the market demand functions for the three cases (assuming price is measured on the x-axis and quantity demanded is measured on the y-axis):
Case 1:
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0 5 10 15 20 25 30
Case 2:
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30 -| /
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20 -| /
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0 5 10 15 20 25 30
Case 3:
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40 -|
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20 -| /
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0 5 10 15 20 25 30
Suppose there are 3 types of consumers with demand: 𝑄𝑑 = 10 − 2𝑝 and 5 types of consumers with demand 𝑄𝑑 = 10 − 5𝑝.
a. Calculate market demand (make sure to consider 3 cases). Sketch the market demand function.
1 answer