Suppose that, holding all else constant, when the price of Good X (Px) is $6, consumers demand 0 units. When the price is $0, consumers demand 3 units. Derive the demand function for Good X based on that information.QDx = Blank 1 Question 9[select: , 0.3333, 3, 1.5, 2, 6] Blank 2 Question 9[select: , -2, -0.25, -1.5, -0.5, -0.05] Px

Question

BlackTom AI · Accepted Answer

To derive the linear demand function for Good X from the given points, I’ll walk through the key steps using a standard linear form Q = a + bP where Q is quantity demanded and P is price.

First, use the information at Px = 0. When the price is 0, quantity demanded is 3 units. Plugging into Q = a + bP gives Q = a + b(0) = a, so a must equal 3. This identifies the intercept as 3, corresponding to Blank 1.

Next, use the information at Px = 6. When Px = 6, Q = 0. Substitute into Q = a + bP with a = 3: 0 = 3 + b(6). Solving for b yields b = -3/6 = -0.5. This gives the slope, which corresponds to Blank 2.

Thus, the consistent linear demand function is Q = 3 - 0.5P. The two requested blanks fill as follows: Blank 1 should be 3 (the intercept a), and Blank 2 should be -0.5 (the slope b).

Common alternative reasoning mistakes to beware of:
- Thinking the slope is negative of the price change over quantity change without solving: simply using two points (0,3) and (6,0) confirms a slope of (0-3)/(6-0) = -3/6 = -0.5, matching the result.
- Misplacing the intercept: if you misinterpret the point at Px = 0, you might incorrectly set the intercept to 0 or to a different value; the given point directly pins a = 3.
- Assuming a non-linear form: with only two data points and a linear relationship implied by standard demand models, the most straightforward form is linear, unless specified otherwise.

In summary, the blanks are filled with 3 for Blank 1 and -0.5 for Blank 2, yielding the demand function Q = 3 - 0.5Px.

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