In: Economics
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!
1. Total Revenue, R = P*Q
Marginal Revenue is
For firm A. Pa= (4000- Qa)/50
so, = (4000- Qa)/50 * Qa
=(4000-2 Qa)/50
For Firm B,
= (3,200- Qb)/160 * Qb
=(3,200- 2Qb)/160
Total MR = (4000-2 Qa)/50 + (3,200- 2Qb)/160
=80-Qa/25 + 20 - Qb/80
=100 - (16Qa+ 5Qb)/ 400
2. For maximum profit output , Put TMR = 0
100 - (16Qa+ 5Qb)/ 400 = 0
100= (16Qa+ 5Qb)/ 400
16Qa+ 5Qb = 40000 .............. (1)
Also, Qa+ Qb = 3200 .............. (2)
Solving the above two equation gives:
Qa = 2181 and Qb = 1019