Question

Quantity demand is (a-p)/b when p<a and 0 when p is >/= to a. The TCi(qi) is 3qi^2. What is the Consumer equilibrium when there is n firms?

Answers

GPT 3.5
To find the consumer equilibrium when there are n firms, we need to determine the quantity demanded by the consumer and the quantity supplied by the firms.

Given that the quantity demand function is (a-p)/b when p<a and 0 when p is greater than or equal to a, we can equate this with the quantity supplied by the firms.

Let's assume that each firm produces the same quantity, q, and there are n firms in total. So, the total quantity supplied by the firms is nq.

Equating the quantity demanded and supplied, we have:
(a - p)/b = nq

To find the consumer equilibrium, we need to solve for q. Rearranging the equation, we get:
(a - p) = bnq

Simplifying further:
q = (a - p)/(bn)

Now, we need to find the minimum-cost quantity for the consumer, which means finding the quantity that minimizes the consumer's total cost, TC.

The consumer's total cost (TC) is given by 3q^2. Substituting the value of q we found earlier:
TC = 3[(a - p)/(bn)]^2

To minimize TC, we need to find the value of q that minimizes this equation.

Finally, the consumer equilibrium occurs when the consumer's total cost is minimized and the quantity supplied by the firms equals the quantity demanded by the consumer.

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