Assume that total demand in a market is 1 and that customers are uniformly spread across the line segment from 0 to 1.There are only two companies in the market and there is no cost or service advantage held be either Firm 1 or Firm 2.Firm 1 locates at point a,and Firm 2 locates at point 1-b as shown in the figure.A customer chooses one firm or the other solely on the basis of distance travelled.

-The demand at Firm 1 is given by
A)a + $\frac { 1 + b - a } { 2 }$
B)a + $\frac { 1 - b - a } { 2 }$
C)a - $\frac { 1 + b - a } { 2 }$
D)a - $\frac { 1 - b + a } { 2 }$

Question

Assume that total demand in a market is 1 and that customers are uniformly spread across the line segment from 0 to 1.There are only two companies in the market and there is no cost or service advantage held be either Firm 1 or Firm 2.Firm 1 locates at point a,and Firm 2 locates at point 1-b as shown in the figure.A customer chooses one firm or the other solely on the basis of distance travelled.
 
-The demand at Firm 1 is given by
A)a + $\frac { 1 + b - a } { 2 }$ 
B)a + $\frac { 1 - b - a } { 2 }$ 
C)a - $\frac { 1 + b - a } { 2 }$ 
D)a - $\frac { 1 - b + a } { 2 }$

Quizplus · Accepted Answer

Since customers choose the closest firm, the demand for each firm will be proportional to the distance between the firm and the midpoint of the two firms. The midpoint is given by (a+1-b)/2. Therefore, the distance from Firm 1 to the midpoint is (a+1-b)/2-a = (1-b-a)/2, and the demand for Firm 1 is proportional to this distance, which gives (1-b-a)/2 + a = a+(1-b-a)/2 = a+(1-a-b)/2 = a+(1-b-a)/2. Thus, the demand for Firm 1 is given by B.

Assume That Total Demand in a Market Is 1 and That