ECONOMICS CANT FIGURE OUT THIS QUESTION TOTALLY NEW TOPIC FO

ECONOMICS: CAN\'T FIGURE OUT THIS QUESTION; TOTALLY NEW TOPIC FOR ME. I WOULD APPRECIATE IF YOU COULD HELP ME OUT THROUGH OUT ....

1. The town of Riverville is divided in two equal parts by a river. 5,000 people live on the west bank and 5,000 on the east bank. There is one movie theater on each side of the river, and both theaters are showing the same film. The marginal cost of showing a film to a consumer is S5. Each consumer has a reservation value for seeing the film of S10. There is a toll of Ss to travel across the bridge (which you only have to pay once on a given day). Movie theaters simultaneously set prices and can only charge prices in whole dollars. When firms offer the same utility for a group of consumers, they will split the market equally. For example, suppose the West theater charges $4 and the East theater charges $5 and s 1. Then all of the people on the west bank will go the West theater, whereas the people who live on the east bank will be split equally between the theaters. If they both charged S5, people would go to the eater on their side of the river (a) Suppose that s =0 (i) What are the pure strategy Nash equilibria with whole dollar pricing? ii) What would be the pure strategy Nash equilibria with continuous pricing? Explain the difference. (b) Suppose that s-2. What are the (pure strategy and symmetric) Nash equilibria? (c) Suppose that s = 4, what are the (pure strategy and symmetric) Nash equilibria? (d) The town is considering removing the toll on the bridge. How much should the movie theaters be willing to bribe town officials to get them to keep a toll of S4 in place?

Solution

Solution: a): s=0 no toll price

if equal price of theater then equal-equal people are divided in east and west side of the river

income of each side is 5000*5 doller

if price of east theater is 5 doller and west theater is 4 doller then people of east side is 2500 & west side is 7500

price of east side is 5*2500 doller & price of west side is 4*7500 doller

b): s=2 the charge of toll

if movies price is equal both side then equal income is 5000*5 doller

if movies price of east is 5 doller and west is 4 doller, then

income of east side theater is 2500*5=12500 doller

income of west side theater is 7500*4=30000 doller

and toll outcome is 2500*2=5000 doller

c): s=4 the charge of toll

if movies price is equal both side then equal income is 5000*5 doller

if movies price of east is 5 doller and west is 4 doller, then

income of east side theater is 2500*5=12500 doller

income of west side theater is 7500*4=30000 doller

and toll outcome from east side people is 2500*4=1000 doller

d): total amount for willing to bribe town official keep toll is =total no. of people* toll price

                                                                                             =2500*4=1000 doller