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: , 0, 48, 6, 90, 30, 60] Blank 2 Question 5[select: , -10, -20, -0.05] P

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BlackTom AI · Accepted Answer

To construct the total demand for prices within the range 0 ≤ P ≤ 3, I’ll sum the individual demands of Annie, Britta, and Jeff, ensuring each person’s quantity is nonnegative in this price interval.

First, compute each individual's quantity as a function of price:
- Annie: qdA = 48 − 8P. This remains positive for P ≤ 6, and since our price range goes up to 3, Annie buys positive quantity throughout.
- Britta: qdB = 12 − 2P. This stays positive for P ≤ 6, so at P up to 3 Britta also buys positive quantity.
- Jeff: qdJ = 30 − 10P. Here the choke price is P = 3, so at P = 3 Jeff buys qdJ = 0, and for P < 3 he buys a positive amount.

Next, add the three quantities to get the total demand at any price in this interval:
Total Q(P) = qdA + qdB + qdJ = (48 − 8P) + (12 − 2P) + (30 − 10P) = 90 − 20P.

Now evaluate the given blanks:
- Blank 1 (QD = ___) asks for the total quantity when P is in the specified range, i.e., the intercept at P = 0 or the general form evaluated in that range. From the expression 90 − 20P, the total quantity at P = 0 is 90, and the linear form is 90 − 20P for all 0 ≤ P ≤ 3. Thus Blank 1 should be 90.
- Blank 2 (slope of the total demand with respect to price) corresponds to the coefficient of P in the total demand function: −20. This slope is negative, reflecting the law of demand (as price rises, total quantity demanded falls).

Therefore, the appropriate selections are 90 for Blank 1 and −20 for Blank 2. The reasoning relies on straightforward addition of individual demand schedules within the price range where each consumer still purchases a nonnegative quantity, and on combining linear demand functions term-by-term.

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