In this problem p is in dollars and q is the number of units

In this problem, p is in dollars and q is the number of units.
Suppose that the demand for a product is given by:

2p²q = 30,000 + 9000p².

(a) Find the elasticity when p = $50 and q = 4506.

(b) Tell what type of elasticity this is. (unitary elastic, inelastic, or elastic)

(c) How would revenue be affected by a price increase?

(A decrease in price decreases revenue, Revenue is unaffected by price, An increase in price increases revenue, An increase in price decreases revenue, A decrease in price increases revenue)

Solution

Given :

2p2q = 30,000 + 9000p²

2q = 15,000 /p + 4,500p

q = 7,500 /p + 2,250p

Now , differentiate , we get:

dq/dp = -7500/p² + 2250 ..................(1)

given p = 50 , q = 4506

then, putting these into (1), we get:

dq/dp = -7500/(50)² + 2250

dq/dp = -7500/2500 + 2250

          = 2,247

Elasticity E = (p/q) * (dq/dp)

E = (50/4506) * (2247)

   = 18,725 / 751

E = 24.933