Question

The total demand of a firms output is given by q=50-0.5p.The demand for the firms output in two markets are:q1=32-0.4p1 and q2= 18-0.1p2.
The total cost of production of the firm is given by c=50+40q.calculate
The total output that the firm must produce in order to maximise profit.
What price must be charged in each market in order to maximise profit.
How much profit would the firm earn if it sold the output as a single price and if the firm discriminate.
The price elasticity of demand for the two markets at the equilibrium price and quantity.

Answer 1

$$p=100-2q$$

$$TR=pq=100q-2q^2$$

$$MR=100-4q$$

$$MC=40$$

$$100-4q=40$$

$$4q=60$$

$$q=15$$

$$p=70$$

$$\pi=TR-TC=100\times15-2\times 225-50-40\times15=400$$

For firm 1

$$p_1=80-2.5q_1$$

$$TR_1=80q_1-2,5q_1^2$$

$$MR_1=80-5q_1$$

$$80-5q_1=40$$

$$q_1=8$$

$$p_1=60$$

For firm 2:

$$p_2=180-10q_2$$

$$TR_2=180q_2-10q_2^2$$

$$MR_2=180-20q_2$$

$$q_2=7$$

$$p_2=110$$