22 Feb

Suppose that there are 1,000 customers uniformly distributed along the 10km of High Street. Thai, a truly delicious Thai restaurant, is the monopoly provider of Thai food in the area and is located smack back in the middle of High Street (i.e. at the 5km point). Each consumer derives a value of £50 from a meal from Thai and buys at most 1 meal per month. Since there is a pandemic, Thai can only do take it away. For each consumer, transport costs are £2 per kilometer. Thai's marginal cost of supplying a dinner is c = £10. There are no fixed costs at this location.

(a) What price per meal with Thai set if it serves the entire market?

(b) What are Thai's monthly profits at this price?

Now suppose that space for rent has opened at the 0km point of High Street.

The rent for this space is £500 per month. Thai cannot move its original store to a new location, but it can open a second restaurant. The new restaurant will have the same marginal production cost as the original restaurant (c = £10). The two locations can set different prices per meal of po and pn where `o' stands for `original' and `n' stands for `new'

(c) Derive a formula for the marginal consumer who is just indifferent between buying from the new restaurant (at the 0km point) and the original restaurant (at the 5km point).

(d) Suppose that Thai fixes the price of the original restaurant (at the 5km point) at the price that serves the entire market. Find the profit-maximizing price for the new restaurant.

(e) Suppose Thai allowed the original store (at the 5km point) to choose any price (not necessarily such that the entire market is served). Without doing any calculations, would you expect the prices at each restaurant to increase, decrease or stay the same compared to part?

Yusra Anees
22 Feb

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