Question

The inverse demand curve for product X is givenby: PX = 25 - 0.005Q + 0.15PY, where PX represents price in dollars per unit, Qrepresents rate of sales in pounds per week, andPY represents selling price of another product Y indollars per unit. The inverse supply curve ofproduct X is given by: PX = 5 + 0.004Q.

a. Determine the equilibrium price and sales of X. Let PY = $10.
b. Determine whether X and Y are substitutes or complements.

Answer 1

(a) $14.56; 2,388.88

(b) Substitute goods

Step-by-step explanation:

Given that,

Inverse demand curve: PX = 25 - 0.005Q + 0.15PY

Inverse supply curve: PX = 5 + 0.004Q

(a) Let PY = $10

For Equilibrium,

Supply = Demand

5 + 0.004Q = 25 - 0.005Q + 0.15PY

5 + 0.004Q = 25 - 0.005Q + 0.15(10)

0.004Q + 0.005Q = 20 + 1.5

0.009Q = 21.5

Q = 21.5 ÷ 0.009

= 2,388.88

PX = 25 - 0.005Q + 0.15PY

= 25 - 0.005(2,388.89) + 0.15(10)

= 25 - 11.94 + 1.5

P = 14.56

(b) PX = 25 - 0.005Q + 0.15PY

Q = (25 + 0.15PY - PX) ÷ 0.005

From the above equation, the coefficient of the price good Y is positive which means that the quantity is positively related with the price of good Y.

Therefore, as the price of good Y increases then as a result demand for good X increases.

Hence, good X and Good Y are substitute goods.