Question

1) The demand function for cheese is given by F(y) = 50 - y, and the cost functions of both firms is given by C(x) = 4x.

A). What would be the output and price, considering the market for cheese is perfectly competitive?

B). What is the market price, industry output, and each firms level of production if there are two cournot firms operating in the market?

C). What is the industry output and market price if the two firms collude with one another?

Answer 1

1. The demand is , and the cost function of both firms is .

A. The marginal cost of both firms would be or . The firm would produce where or , which is the supply curve of individual firm. The market supply would be also , since each firms can produce infinite products for p=4, both firms would do the same.

The market equilibrium would be where the demand and supply are equal. Solving for both and , we have or as equilibrium quantity and or as equilibrium price, in case the market is competitive.

B. In case the market is Cournot duoply, the best response functions (BRF) are needed to find the required values. The demand function in this case is or , for y1 and y2 are the output of two firms.

The MR of firm 1 would be or or or . The MC of firm 1 is found as . Hence, the firm would produce where its marginal cost is equal to the marginal revenue, ie where or or or , which is the BRF of firm 1.

The MR of firm 2 would be or or or . The MC of firm 1 is the same . Hence, the firm would produce where its marginal cost is equal to the marginal revenue, ie where or or or , which is the BRF of firm 2.

The equilibrium output would be where the BRF's of the firms becomes equal. Solving for both, we have or or or units. Since , we have or or units. Hence, the equilibrium price would be or or dollars. The equilibrium quantity would be or units.

C. If the two firms collude, then they would act as a single firm, and the market output would be that of a monopoly. The MR is or . Their combined MC would be . The equilibrium output would be where MC is equal to the MR, ie or or units. The equilibrium price would be correspondingly or dollars.