Burger King is a US-based fast food restaurant chain. Burger King advertises, de
ID: 1203400 • Letter: B
Question
Burger King is a US-based fast food restaurant chain. Burger King advertises, develops new foods, and procures ingredients, but it owns almost none of the actual restaurants. Instead, the restaurants are owned by franchisees. Assume that each local franchise is a local monopolist with demand of q = 1000 - 200p_H hamburgers per day, where p_H is the price of hamburgers. Assume that franchises are free to set whatever price/quantity they want, but they purchase ingredients at price p_I per hamburger from Burger King. Ingredients are the franchises only variable costs. Burger King can procure ingredients at marginal cost c = 1. For part D, assume that the franchise agreement is a two-part tariff with (daily) fixed price L and ingredient price p_I per hamburger. What L and p_I maximize Burger King's profits, and what p_H maximizes the franchise's profits?Explanation / Answer
In a two-part tariff model, the monopolist sets the usage cost (here, ingredient price) equal to its Marginal cost (MC), and the fixed cost is the entire consumer surplus it can obtain by setting price equal to MC.
So, ingredient price p1 = MC = 1
Demand function: q = 1,000 - 200p
So, when p = 1, q = 1,000 - 200 = 800
When q = 0, pH = 1,000 / 200 = 5 [Reservation price]
Consumer surplus = L = Area between demand curve & price
= (1/2) x (5 - 1) x 800
= (1/2) x 4 x 800
= 1,600
Demand: q = 1,000 - 200pH
200pH = 1,000 - q
pH = 5 - 0.005q
For a franchise, profit is maximized by equating MR with MC.
Total revenue, TR = q x pH = 5q - 0.005q2
Marginal revenue, MR = dTR / dq = 5 - 0.01q
Equating this with MC,
5 - 0.01q = 1
0.01q = 5
q = 500
When q = 500, pH = 5 - (0.005 x 500) = 5 - 2.5 = 2.5 per hamburger
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