Question

A firm sells in two separate markets, A and B. The demand functions in the two Markets are:

Qa=4,000-50Pa and Qb=3,200-160pB.

The total Marginal revenue function is:

1. MRT=_____________________

2. If the firm wants to produce 3,200 units of output, in order to maximize revenue from this output it should produce_____units in plant A and_____units in B.

3. The firm wishes to practice price price discrimination. The firm's marginal cost functions is MC=12.58+0.004Qt

a. To Maximize profit the firm would produce a total of_____units of output.______units would be sold in market A and_____ units in B.

b.The firm would charge a price of_____in market A and a price of _____in B.

c. In quilibrium the demand elasticity is______ in A and ______in B. (Hint: use the E=P/(P-a) formula). This relation would be expected because ______ if greater than_____.

Please show steps. Thank you!

Answer 1

1. Total Revenue, R = P*Q

Marginal Revenue is

For firm A. P_a= (4000- Q_a)/50

so, = (4000- Q_a)/50 * Q_a

=(4000-2 Q_a)/50

For Firm B,

= (3,200- Q_b)/160 * Q_b

₌(3,200- 2Q_b)/160

Total MR = (4000-2 Q_a)/50 + (3,200- 2Q_b)/160

=80-Q_a/25 + 20 - Q_b/80

=100 - (16Q_a+ 5Q_b)/ 400

2. For maximum profit output , Put TMR = 0

100 - (16Q_a+ 5Q_b)/ 400 = 0

100=  (16Q_a+ 5Q_b)/ 400

16Q_a+ 5Q_b = 40000 .............. (1)

Also, Q_a+ Q_b = 3200 .............. (2)

Solving the above two equation gives:

Q_a = 2181 and Q_b = 1019