Question

1.

If a firm's profit is given by  π = -150 + 360Q - 36Q² , then its optimal output is

	a.	36 units.
	b.	2 units.
	c.	20 units.
	d.	12 units.
	e.	5 units.

2.

For a good that has a price elasticity of demand of -1.5 and a marginal cost of $50 per unit, the profit-maximizing price should be

	a.	$50
	b.	$150
	c.	$200
	d.	$168
	e.	$134

3.

If dπ/dQ = 0, how do we know if we have a maximum point as opposed to a minimum point?

	a.	The second derivative must also equal zero for it to be a maximum point.
	b.	The second derivative must be negative.
	c.	None of the above
	d.	The second derivative must be positive.
	e.	The second derivative must be between -1 and +1.

Answer 1

1)

= - 150 + 360Q - 36Q²  

d/dQ = 360 - 72Q

put  d/dQ = 0

360 - 72Q = 0

360 = 72Q

Q = 360/72

Q = 5

SOC

d²/dQ² = - 72 < 0

So optimal output is Q = 5

(e) is the correct option.

2)

Ed = - 1.5

MC = 50

Profit maximising condition

MR = MC

P(1 - 1/|Ed|) = MC

P(1 - 1/|-1.5|) = 50

P(1 - 1/1.5) = 50

P(1 - 2/3) = 50

P/3 = 50

P = 150

Profit maximising price is $ 150

(b) is the correct option.

3)

If d/dQ = 0 and to have a maximum point  

The second derivative must be negative that is  d²/dQ² < 0

(b) is the correct option.