Annie's demand for latte's is given by the individual demand function: qda= 48-8P. Annie's choke price is $6.Britta's demand for latte's is given by the individual demand function: qdb= 12-2P. Britta's choke price is also $6.Jeff's demand for latte's is given by the individual demand function: qdj = 30-10P. Jeff's choke price is only $3.Find the total demand function for prices less than or equal to $3 but greater than or equal to $0.QD = Blank 1 Question 5[select: , 6, 48, 30, 0, 60, 90] Blank 2 Question 5[select: , -0.05, -10, -20] P多重下拉选择题
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Question

Annie's demand for latte's is given by the individual demand function: qda= 48-8P. Annie's choke price is $6.Britta's demand for latte's is given by the individual demand function: qdb= 12-2P. Britta's choke price is also $6.Jeff's demand for latte's is given by the individual demand function: qdj = 30-10P. Jeff's choke price is only $3.Find the total demand function for prices less than or equal to $3 but greater than or equal to $0.QD = Blank 1 Question 5[select: , 6, 48, 30, 0, 60, 90] Blank 2 Question 5[select: , -0.05, -10, -20] P多重下拉选择题

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BlackTom AI · Accepted Answer

To determine the total demand for the three consumers at prices between 0 and 3, I will add their individual demand functions.

First, Annie's demand is qA = 48 − 8P.
Second, Britta's demand is qB = 12 − 2P.
Third, Jeff's demand is qJ = 30 − 10P.

The total quantity demanded at a given price P is QD = qA + qB + qJ = (48 − 8P) + (12 − 2P) + (30 − 10P).

Now I combine like terms: the constant terms sum to 48 + 12 + 30 = 90, and the P-coefficients sum to (−8) + (−2) + (−10) = −20. Therefore, QD = 90 − 20P.

Since the problem asks for prices less than or equal to $3 and greater than or equal to $0, this formula applies in that price range because all three individuals have positive quantities at P ≤ 3 (Jeff’s choke price is 3, so at P = 3 his quantity is qJ = 30 − 10×3 = 0, while Annie and Britta still have positive quantities).

Evaluating the blanks: at P = 0, QD = 90, which matches the option 90. The slope with respect to price is −20, so the coefficient for P is −20.

Thus, the total demand function over the specified price interval is QD = 90 − 20P.

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