Suppose that the (inverse) demand curve for Cranberries is given by P=40−6QP=40−6Q and TC=$4Q+$3Q2TC=$4Q+$3Q2.

a. What are four conditions required for a competitive market?

b. What is the equilibrium price, quantity, and profit if the market is competitive?

c. What is the equilibrium price, quantity, and profit if there are two firms in the market (note Q=q1+q2Q=q1+q2)?

d. What is the equilibrium price, quantity, and profit if there is a monopoly in the market (note Q=QQ=Q)?

e. If there were 3 firms, where do you estimate the output and the price to be? This does not require a mathematical calculation; it is based on the expectations created by the prior three answers.

a.

Conditions of the competitive market:

There should be presence of multiple buyers and sellers.

The price should be equal to marginal cost, without any additional markups.

Both sellers and buyers have complete information about the market.

There are no restrictions on entering or leaving the market.

b.

If the market is competitive, the equilibrium price (p) is equal to marginal cost (MC) for maximizing profit.

p=MCTC=4Q+3Q2=4+6Q40−6Q=4+6QQ=3p=40−6(3)=22PF=TR−TC=(22)(3)−4(3)−3(3)2=27p=MCTC=4Q+3Q2=4+6Q40−6Q=4+6QQ=3p=40−6(3)=22PF=TR−TC=(22)(3)−4(3)−3(3)2=27

The equilibrium price is $22, quantity is 3 and profit(PF) is $27.

c.

If the market is duopoly, the equilibrium price (p) is at where marginal revenue is equal to marginal cost (MC) for maximizing profit for each q.

Q=q1+q2P=40−6QP=40−6q1−6q2TR1=40q1−6q12−6q1q2PF=40q1−6q12−6q1q2−4q1−3q12=36q1−9q12−6q2dPFdq1=36−18q1−6q2=0q1=2−0.33q2Q=q1+q2P=40−6QP=40−6q1−6q2TR1=40q1−6q12−6q1q2PF=40q1−6q12−6q1q2−4q1−3q12=36q1−9q12−6q2dPFdq1=36−18q1−6q2=0q1=2−0.33q2

Similarly, for q2:

q2=2−0.33q1q2=2−0.33q1

Substituting q2 in q1,

q1=2−0.33q2=2−0.33(2−0.33q1)=2−0.66−0.1q11.1q1=1.34q1=1.23q2=2−0.33(1.23)=1.6Q=1.23+1.6=2.83P=40−6(2.83)=23.02PF=36q1−9q12−6q2=36(1.23)−9(1.23)2−6(1.6)=21.06q1=2−0.33q2=2−0.33(2−0.33q1)=2−0.66−0.1q11.1q1=1.34q1=1.23q2=2−0.33(1.23)=1.6Q=1.23+1.6=2.83P=40−6(2.83)=23.02PF=36q1−9q12−6q2=36(1.23)−9(1.23)2−6(1.6)=21.06

The equilibrium price is $23.02, quantity is 2.83 and profit is $21.06.

d.

In monopoly profit is maximum at Marginal revenue(MR) and Marginal cost (MC):

MR=MC40−12Q=4+6Q18Q=36Q=2P=40−6(2)=28PF=TR−TC=(28)(2)−4(2)−3(2)2=$36MR=MC40−12Q=4+6Q18Q=36Q=2P=40−6(2)=28PF=TR−TC=(28)(2)−4(2)−3(2)2=$36

The equilibrium price is $28, quantity is 2 and profit is $36.

e.

The 3 firm market would be oligopolistic market, a step further to duopoly given in part c. The market equilibrium output Q will be given as q1+q2+q3 and that will be less than the duopoly output. Equilibrium price will be less than duopoly price and profit will be less than duopoly market.