Question

Pamela owns a miniature-golf course. Her weekly fixed costs of operation are $1000, while her variable costs are 0. Pamela has two types of clients, serious players and occasional players. There are 100 customers of each type, and the individual weekly demand functions for miniature golf games are:

Demand serious player: qd = 10 – P

Demand occasional player: qd = 5 – P/2

a) Pamela believes that she will make the most possible profit by catering only to the serious players. She will price using a two-part tariff, where she will charge a weakly fee for access to her golf courses and a usage fee per game played of miniature-golf. What access fee and usage fee will Pamela charge? What will be Pamela’s profit? Why would occasional players not want to go to Pamela’s golf course, if she charges the fees you found above?

b) Borat, a good friend of Pamela, advises her that she probably would increase her profits by having both types of players in her golf course. Pamela is still restricted to using the same two-part tariff for everyone. What will be the access fee and the entry fee Pamela will charge? What is her profit in this case?

Answer 1

A) using two part tariff( when taking one type into consideration)

She will set usage price equal to marginal cost. And set Access fee equal to Consumer surplus at this price.

Because marginal cost=0, so per unit usage price=0

Access fee=1/2*10*10=50

Total revenue=50*100=5000

Profit=5000-1000=4000

At P=0, occasionall player Consumer surplus=1/2*5*10=25

So Access fee is higher than their total willingness to pay ,so that why they won't buy.

B) she will use occasional player demand to calculate access fee as ,if she use serious player demand to calculate access fee ,then it will go high that occasional playe won't buy.

Access fee= Consumer surplus=1/2*(5-0.5p)*(10-p)=0.5(50-5p-5p+0.5p^2)=25-5p+0.25p^2

Total profit=200*access fee +100*p*(10-p)+100*p*(5-0.5p)

Total profit=200*access fee+100p*(15-1.5p)=200*(25-5p+0.25p^2)+1500p-150p^2-1000

Profit=4000-1000p+50p^2+1500p-150p^2

Derivative of profit with respect to p,

∆profit/∆p=-1000+100p+1500-300p=500-200p

Put derivative of profit equal to zero to find profit maximizing price.

500-200p=0

P=-500/-200=2.5( usage fee)

Access fee=25-5*2.5+0.25*2.5*2.5=14.0625

Q( serious)=10-2.5=7.5

Total demand ( serious)=100*7.5=750

Q( occasional)=5-0.5*2.5=3.75

Total demand ( occasional)=100*3.75=375

Total market demand=750+375=1125

Total revenue= 200*14.0625+2.5*1125=2812.5+2812.5=5625

Profit=5625-1000=4625