Over the last two years, there has been increasing attention paid to Australia’s franchise system. Many franchisees appear to be under significant financial distress and the industry is so fraught with disagreements that the ACCC has setup its own website page to try to educate potential franchisees about the risks in entering into a franchise agreement.

Misaligned Incentives In the attached article from Ad Age (https://adage.com/article/cmo-strategy/mcdonald-s-franchisees-dump-delivery/316684), McDonald’s and its franchisees are engaged in an ongoing dispute over remodeling requirements for existing restaurants and fees associated with delivery. The following problem is designed to think about these issues in more detail.

Ann is a monopoly franchisee of “Bob’s Best Burgers” and owns a single restaurant. The franchisee can choose to make an investment I ∈ [0, 240] to retrofit her restaurant which will increase the overall quality of the dining experience. Based on calculations from similar restaurants, if Ann chooses an investment level I, she faces an (inverse) demand curve of:

P(Q, I) = 120 + 2I − Q,

where P is the price that can be charged given an investment of I and an amount of food sold Q. Ann has written a contract with Bob that promises 50% of revenue in exchange for usage of the brand. Thus, Ann’s total revenue is given by

R(Q, I) = 1/2*(120 + 2I − Q)*Q.

Given Q units of food sold and an investment of I, the franchisees costs are given by:

C(Q, I) = 1/2*Q² + 1/2*I² + 200.

The franchisee is thus trying to maximize: π_A(Q, I) = R(Q, I) − C(Q, I) = 1/2 [(120 + 2I − Q)Q − Q² − I² − 400]

Question 1:

Graph the (inverse) demand function when I = 30 and I = 60. Using the graph, show what price Ann could set if she wanted to sell 120 units with each investment level. Suppose that Ann is trying to maximize her own profits. Find the quantity Q and investment I that maximizes her profits.1 How much profit does Ann make? How much profit does Bob make?

Note: This problem requires the use of a partial derivative. To solve the problem, fix the Quantity Q and maximize profit with respect to I. Next, fix the investment I and maximize profit with respect to Q. Use the two resulting equations to find the best Q and I.

Question 2:

Suppose that as part of the contract, Bob (the franchisor) is allowed to enforce any investment level I that he sees fit but cannot prevent Ann from shutting down if her franchise is not profitable. For any I, Bob’s profit is equal to πB(Q, I) = 1 2 (120 + 2I − Q(I))Q(I), where Q(I) is the quantity Ann chooses to sell given that she is forced to invest I. What investment level should Bob choose if he wishes to maximize his profits? What quantity and price does Ann chose? What is Bob’s profit in this case? You should assume in this problem that the 200 is a fixed cost that can be saved if Ann shuts down.

Question 3:

Suppose that Bob is able to offer a contract where he does not take a share of Ann’s revenue but instead requires Ann to pay a fixed franchise fee of K. If the maximum amount of investment Ann can put in is I = 240, what is the largest fixed franchise fee that Bob could charge Ann?2 Could Bob do better if he also tried to constrain Ann’s investment choice?

Question 4:

Suppose Ann converts her agreement to one where she agrees to pay Bob 80, 000 to operate her franchise over the next 10 years with no revenue sharing. In the second year of this contract, Bob is approached by Charles who wishes to open a “dark restaurant” which will deliver Bob’s Best Burgers to customers at home from a warehouse location that has no shop front. Why are these dark restaurants likely to provide delivery services at lower cost? Explain how Bob’s incentives have changed as a result of Ann’s decision to convert her contract. Why is Ann’s restaurant likely to continue to run even if the new delivery service cannibalizes her customers.