In a large city, both sellers (convenience stores, say) and consumers are evenly spread out. There is no market power on either side and the equilibrium price for "one purchase" at a convenience store is 100. The cost of walking to and from a store is 10x, where x is the distance in kilometers among the consumer's home and the store. The marginal cost is equivalent for all stores at 60; the markup covers the fixed costs (rents, staff etc). In the competitive equilibrium, the average transport distance is small & positive, but can be assumed to be approximately 0. Consumers will buy where the total price, equivalent to the sum of the purchase and the cost of walking, is the smallest. I.e., all stores are identical, except for their location.
a) Use the SSNIP-test methodology to verify the size of the geographical market by measuring how large a (circular) area must be for a uniform (the same in the whole area corresponding to the hypothetical market) price increase by 10 % above the competitive price to be profitable for a hypothetical monopolist, with the above assumptions. As a first step, set up an expression that shows which consumers will pay the higher price and which will incur a cost of walking to avoid paying the higher price.
b) Do the similar, under the assumption that the marginal cost of production is 100.
c) Suppose that the city is larger than the size of the relevant geographical market as estimated in a) and b). talk about the arguments that can imply that the relevant geographical market can be city-wide (or national), despite your findings. You are not permitted to change the basic assumptions of costs and equilibrium prices above, but you can add other considerations. Are there arguments that work in the opposite direction, so that the true relevant market may be smaller than what you found?