Question

21. A commodity is being traded on the exclusive market and the demand function for it is given as follows. P=1/3Q+40
And let's say the marginal cost of producing this product is always constant at 10. Find the price and output that the monopoly maximizes profit.

plz write neatly and brieftly and clearly
i cant understand cursvie handwriting

demand equation  

p=(-1/3)Q+40

Answer 1

The given demand function is

P=-Q/3+40

The Marginal Cost is given at 10.

The monopolist will maximize the profit where Marginal Cost=Marginal Revenue.

We know that

Revenue=Price*Quantity

Using the demand equation, we get

Revenue=(-Q/3+40)*Q=-Q²/3+40Q

Marginal Revenue would be the differentiation of the revenue. Differentiating above equation, we get

MR=-2Q/3+40

Equating this to MC, which is 10.

10=-2Q/3+40

Rearranging, we get

2Q/3=30

Q=90/2

Q=45

Price at this level, using the emand equation and Q=45, will be

P=-45/3+40

P=40-15

P=25

So, profit will be maximized when

Q=45 and Price=25