Question

Joe has just moved to a small town with only one golf​ course, the Northlands Golf Club. His inverse demand function is

p=140−2​q,

where q is the number of rounds of golf that he plays per year. The manager of the Northlands Club negotiates separately with each person who joins the club and can therefore charge individual prices. This manager has a good idea of what​ Joe's demand curve is and offers Joe a special​ deal, where Joe pays an annual membership fee and can play as many rounds as he wants at ​$40, which is the marginal cost his round imposes on the Club. What membership fee would maximize profit for the​ Club? The manager could have charged Joe a single price per round. How much extra profit does the Club earn by using​ two-part pricing?

The​ profit-maximizing membership fee​ (F) is

​$_________.

​(Enter your response as a whole​ number.)

Answer 1

Under two part pricing in order to maximize profit a firm should charge Price = Marginal Cost and whatever consumer surplus consumer is earning, producer or firm should charge this consumer surplus as membership fee.

Here MC = marginal cost = 40. Hence P = MC = 40 and q = (140 - 40)/2 = 50

Now lets calculate Joe's consumer surplus.

Consumer surplus is the area Below demand curve and above price line. Price line is P = MC = 40.

When Q = 0 => p = 140(Vertical intercept)

Hence Consumer Surplus = (1/2)(140 - 40)50 = 2500

hence, The​ profit-maximizing membership fee​ (F) is $2500

Under two part pricing P = MC and hence Profit = membership fee = $2500

Under single pricing a producer produces that quantity at which MR= MC

MR = d(pq)/dq = 140 - 4q and MC = 40 =. 140 - 4q = 40 => q = 25. Hence p = 90.

Hence Profit = 90*25 - 40*25 = $1250.

hence Under 2 part pricing he will earn 2500 - 1250 = $1250 more profit.