Question

The demand for good X is given by

Q_X^d = 6,000 - (1/2)P_X - P_Y + 9P_Z + (1/10)M

Research shows that the prices of related goods are given by P_y = $6,500 and P_z = $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.

Good Y is:  (Click to select)  a substitute  neither complement nor substitute  a complement  .

Good Z is:  (Click to select)  a complement  a substitute  neither complement nor substitute  .

b. Is X an inferior or a normal good?

Good X is:  (Click to select)  an inferior good  neither a normal nor an inferior good  a normal good  .

c. How many units of good X will be purchased when P_x = $5,230?



d. Determine the demand function and inverse demand function for good X. Graph the demand curve for good X.

Instruction: Enter all values as integers, or if needed, a decimal rounded to one decimal place.

Demand function: ( ) - ( ) P_X

Inverse demand function: P_X = ( ) - ( ) Q_X^d

Instruction: Use the tool provided 'D' to graph the inverse demand curve from Q_X = 0 to Q_X = 6,000 (two points total).

Answer 1

a) A good Y is a compliment (because the price coefficient of a good Y is negative), and a good Z is a substitute. (Because the price coefficient of commodity Z is positive).

b) Good X is a normal good.

c) When P_x = $5,230

$$ \begin{aligned} &\begin{aligned} Q x^{\mathrm{d}} &=6,000-(1 / 2) \mathrm{P} \mathrm{x}-\mathrm{Py}+9 \mathrm{Pz}+(1 / 10) \mathrm{M} \\ &=6,000-0.5 \mathrm{Px}-\mathrm{Py}+9 \mathrm{Pz}+0.1 \mathrm{M} \\ \mathrm{Q} \mathrm{x}^{\mathrm{d}} &=6,000-0.5 * 5,230-6,500+9^{*} 100+0.1 * 70,000 \\ &=6,000-2,615-6,500+900+7,000 \\ \mathrm{Q} \mathrm{x}^{\mathrm{d}} &=4785 \mathrm{units} \end{aligned}\\ &\text { d) Demand function: } Q x^{d}=-\operatorname{Px}\\ &\text { Inverse demand function: } \mathrm{Px}=-\mathrm{Q} \mathrm{x}^{\mathrm{d}} \end{aligned} $$