Question

9. Customers are uniformly located along a street with unit length (the left end is 0 and the right end is 1). Each of them wants to buy one unit of a good. The transportation cost of customers is c dollars per unit length. Firms have same production cost and the market price is fixed at some level above the production cost.

9 and10

Answer 1

Ans (9) a) if there is 4 firm then average distance for each of the firm will be 1/4 so the equilibrium location for the firm will be 1/2 from left or right whichever i .e, half of the total distance will be equilibrium location.

(a)( ii) yes the location is efficient as this will cost all the firm same so the equilibrium in the market will be maintained.

(b) (i) If there is 5 firms in the market then the distance will be 1/5 and the equilibrium location will be 2/5 of the right.

(b) (ii) This location is efficient

Ans (10) price per quantity for both firm will be :

( 0.2c+ 0.8c)q

dp/dq = 0.2c+ 0.8c

= $1c  

Profit : p.q -c

$1c.q -c where c(q) = mq

= 0 ( profit will be 0 in this location for both the firm)

Ans 10(ii ) P =( 0.2c+ 1c)q

dp/dq = 0.2c +1c

= 1.2 c

Profit = p.q - c

= 1.2cq- c where c = mq

0.2 ( profit per unit of quantity for both the firms )