The demand for company X’s product is given by: Qdx = 12 – 3 Px – 4Py + 1M + 2Ax

Question

The demand for company X’s product is given by:

Qdx = 12 – 3 Px – 4Py + 1M + 2Ax

Where the A variable represents the amount of advertising on good X, Px is the price of good X, Py is the price of good Y, and M is income. Good X sells at $2 per unit, good Y sells for $1 per unit, the company utilizes 2 units of advertising, and consumer income is $10.

Show work and explain why you derived at the answer:

a. How much of good X is purchased by consumers?

b. Are goods X and Y substitutes or complements?

c. Is good X a normal or inferior good?

d. Find an equation for the demand curve and the inverse demand curve.

Explanation / Answer

Qdx = 12 – 3 Px – 4Py + 1M + 2Ax

Qx = 12-3*2-4*1+1*10+2*2 = 16 units purchased by consumers

Cross elasticity = (dQx/dPy)*(Py/Qx) = -4*1/16 = -0.25, somewhat complements with negative cross elasticity

Income Elasticity = (dQx/dM)*(M/Qx) = 1*10/16 = =0.625 normal commodity

Qx = 12-3Px -4*1+1*10+2*2

Qx = 22 - 3Px

3Px = 22-Q

Px = 22/3 - Q/3

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