Zambian Breweries sells its products in Zambia and three neighboring countries. Data collected from 2010 to...

Zambian Breweries sells its products in Zambia 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 Kwacha) 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.

Solutions

Expert Solution

(a)

Revenue = PQ = (-0.3224Q+245.4031)Q

To maximize revenue we take the FOC wrt Q and equate it to 0 (MR =0)

=> 245.4031 = 2*0.3224Q

=> Q = 245.4031/ 2*0.3224 = 39.55 = 40

(b) The firm will maximize profit at a point where MR = MC

TC = 101.1995Q+4699.3441

=> MC = 101.1995

Thus, at profit max we have,

245.4031 - 2*0.3224Q = 101.1995

=> Q = (245.4031 - 101.1995)/ 2*0.3224

= 23.24 = 23

Thus, P = -0.3224*23+245.4031 = 237.98

Rahul Sunny answered 2 years ago

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