In: Economics
Heineken sells its products in Namibia and three neighboring countries. Data collected from 2010 to 2018 shows that the company produced 300,000 barrels of beer annually. During this period, the average price per barrel of beer P (in Namibian dollars) was related to the quantity of beer sold Q (in thousands of barrels) by the demand function
P=-0.3224Q+245.4031
The total cost of producing Q thousand barrels of beer was
TCQ=101.1995Q+4699.3441
At what output level revenue be maximized?
Find the quantity and price levels that maximize profit.
(I)
P = - 0.3224Q + 245.4031
TR = PQ = - 0.3224Q2 + 245.4031Q
Revenue is maximized when MR = dTR/dQ = 0
- 0.6448Q + 245.4031 = 0
0.6448Q = 245.4031
Q = 380.59
(II)
MC = dTC/dQ = 101.1995
Profit is maximized when MR = MC.
- 0.6448Q + 245.4031 = 101.1995
0.6448Q = 144.2036
Q = 223.64