Question

Answers Given Please Show Work

Two hot-dog shops with constant average and marginal costs c= 0 are located on a street of length 1. Let x = 0 represent the west end of the street and let x = 1 represent the east end. The location of shop 1 is 21 = 0.3 and the location of shop 2 is x2 = 0.6. Consumers are located uniformly along the street. Every consumer purchases one hot-dog and they choose which shop to visit based on distance traveled and price. If the consumer travels a distance d and pays a price p, the utility they get is: u=1-d? - p Question 13 Derive the demand curve for shop 2 in the form of 2 = A - Bp2 + Cp1. What is the value of B? A 0.1667 B 0.6667 C 1.167 D 1.667 Find the Nash equilibrium price charged by shop 2. Question 14 A 0.21 B 0.31 C 0.41 D 0.51 Question 15 Suppose travel costs go down, i.e. the cost of d on utility goes down. Assuming the shop locations stay fixed, what would happen to Nash equilibrium prices? A Prices for both shops would go down. B Price for shop 1 goes down, price for shop 2 goes up. C Prices for both shops would go up.

Answer 1

Ans The demand of q2 is based on location as shown in question. The transport cost is not given and after solving the above question we will get the slope of p2 = 1.667

And the Nash equilibrium price for shop 2 is = 0.31

According to formula p2=

(x2- x1 )/3 (4l - x1- x2)

Where x1& x2 are location which are given in question

X1= 0.3

X2= 0.6

And l is the total of location which is given = 1

So putting the value in the equation we get :

(0.6- 0.3)/3 (4*1-0.3-0.6)

0.3/3 (4-0.9)

1/10(3.1)

= 0.31

If the travel cost down then the price for both shops goes down and profit will also goes down

According to this model if transport cost is 0 then profit is also 0 for both the firm ad if transport cost increasing then profit is also increasing.

The total demand will be :

P1 + (x1 - X )²= p2 + (x2- X)²

X= x1+x2/2 + p2- p1/2(x2- x1)

X= 0.45 +( 0.31 - 0.09)/ 0.6

X = 0.45+ 0.3667

~ 0.8167