Question

you assume that Coca-Cola company is the representative firm & has a total cost given by TC= 125+q2+q where q is the quantity of the output that the firm produces. You further assume that the market demand for Coca-Cola products is given by the equation P= 1250.5-2Q, where Q is the entire market quantity. In addition, you are informed that the supply curve for the market is given by P=150+Q.

d) In this market, what is the long run equilibrium price and what is the long run equilibrium quantity for Coca-Cola Company to produce? Explain your answer.
e) Given the long run equilibrium price calculated in part (d) above, how many units of the coca-cola products are produced in this market?

Answer 1

TC = 125 + q^2 + q, demand P = 1250.5 - 2Q, supply P = 150 + Q.
d) The long run equilibrium price and quantity are at point where P = MC = ATC = TC/q, so:
2q + 1 = 125/q + q +1,
q = 125/q,
q^2 = 125,
q = 11.2 units.
P = ATC = 125/11.2 + 11.2 + 1 = $23.36
e) Given the long run equilibrium price P = $23.36 calculated in part (d) above the number of the coca-cola products produced in this market is:
23.36 = 150 + Q,
Q = -126.64, so no coca-cola products are produced in this market.