Suppose we postulate a linear demand curve and observe, through supply shifts, two points on the demand curve. At point $\mathrm { A } , \mathrm { P } ^ { \mathrm { A } } = 2$ and $\mathrm { Q } ^ { \mathrm { AA } } = 6$. At point $\mathrm { B } , \mathrm { P } ^ { \mathrm { B } } = 4$ and $\mathrm { Q } ^ { \mathrm { dB } } = 2$. The choke price for this demand curve is
A) 10
B) 2
C) 5
D) $- 2$

Question

Quizplus · Accepted Answer

To find the choke price, we need to find the price at which the quantity demanded becomes zero, which occurs at the x-intercept of the demand curve.

We can use the two points given to find the equation of the demand curve in slope-intercept form:

Slope = (6-2)/(2-4) = -2

Using point A, we can solve for the y-intercept:

6 = (-2)(2) + b

b = 10

Therefore, the equation of the demand curve is Q = 10 - 2P.

To find the choke price, we set Q = 0 and solve for P:

0 = 10 - 2P

P = 5

Therefore, the choke price is $5. The choke price is the price at which quantity demanded is zero. To find the choke price, we need to find the x-intercept of the demand curve, which we can do by solving for P when Q = 0.

Using the two points on the demand curve, we can find the slope of the line:
slope = (Q^B - Q^A) / (P^B - P^A) = (2 - 6) / (4 - 2) = -2

Using the slope-intercept form of a linear equation, we can write the demand curve as:
Q = -2P + b

To solve for b, we can use one of the points, say point A:
6 = -2(2) + b
b = 10

So the demand curve is:
Q = -2P + 10

Setting Q = 0, we have:
0 = -2P + 10
P = 5

Therefore, the choke price is $5.

Suppose We Postulate a Linear Demand Curve and Observe, Through A,PA=2\mathrm { A } , \mathrm { P } ^ { \mathrm { A } } = 2A,PA=2

Suppose We Postulate a Linear Demand Curve and Observe, Through $\mathrm { A } , \mathrm { P } ^ { \mathrm { A } } = 2$