Question

p=160−2q 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 $20, which is the marginal cost his round imposes on the Club. Joe marries Susan, who is also an enthusiastic golfer. Susan wants to join the Northlands Club The manager believes that Susan's inverse demand curve is p=140−2q The manager has a policy of offering each member of a married couple the same two-part prices, so he offers them both a new deal. What two-part pricing deal maximizes the club's profit? Will this new pricing have a higher or lower access fee than in Joe's original deal? How much more would the club make if it charged Susan and Joe separate prices? The club maximizes profit subject to the policy by charging a per round price of p=$ and a lump-sum fee of F=$ (Enter your responses as whole numbers.) The profit-maximizing membership fee (F) in Joe's original deal (without the same prices for each member of a married couple) is $ (Eriter your response as a whole number.) The Club's extra profit from charging different two-part tariffs (above what its profit would have been from charging the same two-part tariff to Joe and Susan) is $. (Enter your rosponse as a whole number.)

Answer 1

The two-part pricing deal to maximize the club's profit involves setting the membership fee to capture the consumer surplus for both Joe and Susan. The original access fee for Joe will typically be lower than the joint deal's fee because of additional surplus from Susan. Separate pricing could increase the club's profit by better capturing individual consumer surpluses.

Step-by-step explanation:

The two-part pricing deal to maximize the club's profit, given the monopolist has set a marginal cost of $20, would involve setting a membership fee (lump-sum fee F) and per round price p such that the total revenue is maximized for both Joe and Susan jointly. Because the problem statement doesn't provide specific numbers for these, we can't calculate exact fees and charges. However, the process to determine these involves calculating the consumer surplus (area under the demand curve above the price) for both Joe and Susan, setting the per round price to the marginal cost of $20, and then capturing the consumer surplus with the membership fee. The original deal with only Joe would typically have a lower access fee compared to a deal with both Joe and Susan because Susan's demand adds additional consumer surplus that the club can capture. If the club charged Susan and Joe separate prices, it could potentially capture more of each individual's consumer surplus, increasing overall profit.

Total revenue, total cost, and profit are calculated to determine the most profitable pricing strategy. For instance, in another scenario shown in step 3 of the given example, total revenue is calculated by multiplying the quantity sold by the price, total cost is obtained by multiplying quantity by average cost, and profit is then found by subtracting total costs from total revenues. For a monopolistic competitor, like the one described for Authentic Chinese Pizza, the firm would decide the profit-maximizing price after determining the output level and consulting the perceived demand curve.