Consider a firm deciding on building a stadium for mass entertainment. Doing so

Question

Consider a firm deciding on building a stadium for mass entertainment. Doing so would cost one million dollars, yielding a stadium that could then seat one hundred thousand people at zero marginal cost. We suppose that forty thousand people are willing to pay $20, while sixty thousand more people are willing to pay $5. (a) How much revenue would the firm make by building the stadium and charging $20? (b) How much revenue would the firm make if it built the stadium and charged $5? (c) What is the most revenue the firm can make? Can it cover the cost of building the 1. stadium? Explain. (d) Suppose the firm could transact costlessly with the potential patrons of the stadium Do you think the firm would end up building the stadium? Explain

Explanation / Answer

Answer 1

a) If a firm charges $20 ten only 40,000 are willing to buy then hence he can only sell only 40,000 seats so his total revenue will be 20*40000 = $800,000.

b) If a firm charges $5 then only 100,000 are willing to buy then hence he can only sell only 100,000 seats so his total revenue will be 5*100000 = $500,000.

c) If the firm can charge only 1 price at a time(i.e. No price discrimination) then we can see from above that firm can earn maximum revenue of $800,000,which is lesser than the total cost of building stadium(1 million). Hence he cannot cover the total cost if he sell at a same price with no price dicrimination If he can do price discrimination details are given in the next part

d) If he can transact constlessly with the potential buyers. Then he will do price discrimination and will charge $5 to 60,000 consumers and will charge $20 to 40,000 consumers. Hence Total Revenue generated will be 40,000*20 + 5*60,000 = 1,100,000. Hence as we can can see that total revenue generated is greater than building the cost($1 million) hence he will build the dam.

Hence The firm will end up building the dam.   

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