The total cost for a product-testing firm is
C(q)=70 + 20q2
q= number of products tested
Price of a product = average cost
Each corporation purchases one product test per year from a product-testing firm in the same city. All other inputs are ubiquitous.
Suppose five corporations are initially distributed uniformly, with one corporation in each city (A,B,C,D,E).
Is the initial distribution a Nash Equilibrium?
Demonstrate it is not by finding how much one corporation would pay if they deviate and move to another city?
What is the average price of having two tests conducted? (Which is the price that the corporation would pay if they "live" in a city where two tests are conducted)
The average price of moving and thus, having two tests is: $_____
The initial distribution is not a Nash Equilibrium because there is an incentive for a corporation to deviate and move to another city where the number of tests is lower.
The average cost per test can be calculated by dividing the total cost by the number of tests:
C(q) = 70 + 20q^2 Average cost per test = C(q) / q
When q = 2, the average cost per test is:
Average cost per test = (70 + 20 * 2^2) / 2 = 70 + 20 * 4 / 2 = 70 + 40 = 110
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