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Let us again consider the monopoly Sreeb but assume it's profit function is:
POs = (370 - Q)Q

What level of diamond production Q does Sreeb choose? Round your answer to one decimal place if necessary.

Let us again consider the monopoly Sreeb but assume its profit function is POs 370 QQ What level of diamond production Q does Sreeb choose Round your answer to class=

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oladayoademosu

The profit function POs = (300 - Q)Q - 10Q

Profit = revenue - cost

Revenue = price × quantity = PQ = (300 - Q)Q

cost = maginal cost × quantity = 10Q

So, Profit, PO = revenue - cost

= (300 - Q)Q - 10Q

So, the profit function POs = (300 - Q)Q - 10Q

The level of diamond production sreeb chooses is Q = 185.

Since the profit function POs = (370 - Q)Q the level of diamond that will produce maximum profit is obtained when we differentiate POs with respect to Q and equate it to zero.

So, dPOs/dQ = d(370 - Q)Q/dQ

= (370 - Q)dQ/dQ + Qd(370 - Q)/dQ

= 370 - Q - Q

= 370 - 2Q

Equating it to zero, we have

370 - 2Q = 0

2Q = 370

Q = 370/2

Q = 185

The level of diamond production Sreeb chooses is Q = 185.

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