If consumer 1 has the inverse demand function given by p = 15 - x and consumer 2 has the inverse demand function given by p = 20 - 3x, then the total quantity demanded by the two consumers is x = 7 when the price p, is 11.

Question

Quizplus · Accepted Answer

We can first plug in the given price of 11 into each of the inverse demand functions:
For consumer 1: 
11 = F1/15 - F1/15x
Multiplying both sides by 15x, we get: 
165x = F1 - F1x
Solving for F1, we get: 
F1 = 165x / (1 + x)

For consumer 2: 
11 = F1/20 - 3F1/20x
Multiplying both sides by 20x, we get: 
220x = F1 - 3F1x
Solving for F1, we get: 
F1 = 220x / (1 + 3x)

The total quantity demanded is the sum of the quantities demanded by each consumer:
F1total = F1 for consumer 1 + F1 for consumer 2
F1total = 165x / (1 + x) + 220x / (1 + 3x)

Simplifying this expression using a common denominator, we get:
F1total = (165x(1+3x) + 220x(1+x)) / (1+x)(1+3x)
F1total = (825x + 770x^2) / (1+4x+3x^2)

When p=11, x=7, so:
F1total = (825(7) + 770(7)^2) / (1+4(7)+3(7)^2) = 2945/101

Thus, the statement is true, since the total quantity demanded when p=11 is approximately 29.06.

If Consumer 1 Has the Inverse Demand Function Given by P