Product Testing

The total cost for a product-testing firm is C(q) = 60 + 10q, where q is the number of products tested. The price of a product test equals the average cost per test, and each corporation in a region purchases one product test per year from a product-testing firm in the same city. All other inputs are ubiquitous (available at the same price at all locations). Suppose five corporations are initially distributed uniformly, with one corporation in each city (A, B, C, D, E).

a. Is the initial distribution a Nash equilibrium? Demonstrate with a suitable unilateral deviation.

b. Describe the Nash equilibrium in terms of (i) the distribution of firms and (ii) the price of a product test