Question

Assume that the demand for a product X is:

Q^d_x = 4,500 – 0.5P_x + P_y – 6P_z + 0.05M,

where P_x is unit price of product X,

P_y is unit price of product Y,

P_z is unit price of product Z, and

M is average income of consumers of product X.

Determine the size of the consumer surplus at $10,500 per unit price of X. Clearly show your steps and manual calculations.

Py = $4,760

Pz = $85

M = $75,000

Answer 1

Qdx = 4,500 - 0.5Px + Py - 6Pz + 0.05M

Py = $4,760

Pz = $85

M = $75,000

Qdx = 4,500 - 0.5Px + 4,760 - (6*85) + (0.05*75,000)

Qdx = 4,500 - 0.5Px + 4,760 - 510 + 3,750

Qdx = 12,500 - 0.5Px

Per unit price of X is $10,500.

Calculate the quantity demanded at price of $10,500 per unit -

Qdx = 12,500 - 0.5Px = 12,500 - (0.5*10,500) = 12,500 - 5,250 = 7,250

Calculate the price when Qdx is 0 -

Qdx = 12,500 - 0.5Px

0 = 12,500 - 0.5Px

0.5Px = 12,500

Px = 12,500/0.5

Px = 25,000

Calculate the consumer surplus -

CS = 1/2 * [(Price when Qdx is 0) - Current price] * Current quantity demanded

CS = 1/2 * [$25,000 - $10,500] * 7,500

CS = 1/2 * $14,500 * 7,500 = $54,375,000

The size of consumer surplus is $54,375,000.