Question

Let x represent the number of items supplied or demanded each month and p represents the unit price of the items (in dollars). Equation A is –2x + 6p = 114 and Equation B is 9x + 3p = 288.

Answer each of the following.
a. Which equation is the demand equation?
b. How many items will consumers purchase if the items are free?

Answer 1

Equation A is the demand equation due to its negative slope relating price and quantity. If the items are free (p = 0), Equation A predicts that consumers will demand 57 items.

Step-by-step explanation:

To determine which equation represents the demand curve and which represents the supply curve, you must understand that the demand curve generally has a negative slope, since the quantity demanded typically decreases as the price increases. Conversely, the supply curve has a positive slope, as the quantity supplied tends to increase with the price. Looking at Equation A (–2x + 6p = 114) and Equation B (9x + 3p = 288), we see that Equation A has a negative coefficient in front of x, which suggests a negative relationship between price and quantity, indicative of a demand equation.

To find the quantity demanded when the price is zero (items are free), set p = 0 in the demand equation. For Equation A, which is the demand equation, this gives us –2x + 6×0 = 114, simplifying to –2x = 114. Solving for x, we find that x = –57, indicating that consumers will demand 57 items when the price is free.