Question

Consider the demand equation where x represents the quantity demanded in units of a thousand and p is the unit price in dollars. p = −x2 + 25 (a) Sketch the demand curve. The graph is -10 until 10 in x axis and the same space for y (b) Determine the quantity demanded when the unit price is set at p = $9.?

Answer 1

Mathematically, the quantity demanded when the unit price is set at $9 is found by solving the equation 9 = −x2 + 25, yielding a quantity demanded of 4,000 units.

Step-by-step explanation:

The student is dealing with a demand equation in the context of economics, but this problem is essentially a mathematical one involving graphs and algebra. Specifically, the demand equation is p = −x2 + 25, where 'x' represents the quantity demanded in thousands of units, and 'p' is the unit price in dollars. For the first part of the question, sketching the demand curve requires plotting this quadratic equation on a graph with p on the vertical axis (price) and x on the horizontal axis (quantity).

When the unit price is set at p = $9, we need to solve the equation for x. Insert the given price into the demand equation:

9 = −x2 + 25

By rearranging and solving for 'x', we find that:

x2 = 16

x = ±4

Since the quantity demanded cannot be negative in this context, we disregard the negative value, which gives us the positive quantity demanded of 4,000 units (since 'x' is in thousands).