1. ## profit maximising monoloys

can anyone help?

A monopoly firm has a total revenue function:
R = 24Q – 2Q2
and a total cost function:
C = Q2 + 5
where R, C and Q are total revenue, total cost and quantity respectively.

(a)Calculate:
i. The monopolist’s profit maximising output and price.
ii. The value of total profit at the profit maximising price and output.
iii. The co-efficient of price elasticity at the profit maximising price and output.
iv. How will your calculations in i. and ii. above be affected by a lump sum tax of 30?

2. arslan, maybe this'll help kick it off for you...

Your profit function $\pi$ , for any Q, is just Revenue less Cost, or

$\pi(Q) = R(Q) - C(Q) = (24Q - 2Q^2) - (Q^2 + 5)$

When you put R and Q together, you'll end up with a single function / equation for profit:

$\pi = -3Q^2 + 24Q - 5$

Now you can see that your profit function is a quadratic, graphically represented by a downward-opening parabola (the leading term has a negative coefficient).

Maximum profit is achieved at the vertex of that parabola. You can determine that vertex using your favorite weapon of choice: Either via algebra (rearrange the equation into "vertex" form), or calculus (find the Q at which the first derivative = 0).

That'll get you running with ball, at least. Best of luck with it!