The demand for good X is given by QXd 6000 12PX PY 9PZ

The demand for good X is given by QXd = 6,000 - (1/2)PX - PY + 9PZ + (1/10)M Research shows that the prices of related goods are given by Py = $6,500 and Pz = $100, while the average income of individuals consuming this product is M = $70,000. a. Indicate whether goods Y and Z are substitutes or complements for good X b. Is X an inferior or a normal good? c. How many units of good X will be purchased when Px = $5,230? d. Determine the demand function and inverse demand function for good X. Graph the demand curve for good X POST A GRAPH of all points

Solution

a) Good Y is a complement(because the price co-officient of good Y is negative) and good Z is a substitute. ( because the price co-officient of good Z is positive).

b) Good X is a normal good.

c) When Px = $5,230

Qx^d = 6,000 - (1/2)Px - Py + 9Pz + (1/10)M

       = 6,000 - 0.5Px - Py + 9Pz +0.1M

Qx^d = 6,000 - 0.5 * 5,230 - 6,500 + 9 * 100 + 0.1 * 70,000

       = 6,000 - 2,615 - 6,500 + 900 + 7,000

   Qx^d = 4785 units

d) Demand function: Qx^d = - Px

    Inverse demand function: Px = - Qx^d