Suppose the total demand function for a good was made up of 10 identical, individual demanders all with a demand function given by: qD = 10 - 0.2P.Find the inverse, total demand function and fill in the missing values below.P = 50 - Answer Question 7[input] QD(Round to the nearest two decimal places if necessary.)

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We start by understanding the setup: there are 10 identical individual demanders, each with qD = 10 − 0.2P, where P is the price and qD is the quantity demanded by one individual.

Step 1: Compute the total quantity demanded by all 10 individuals at price P.
- Since individuals are identical and demand sums across buyers, total QD = 10 * qD_individual = 10 * (10 − 0.2P).
- Multiply out: QD = 100 − 2P.

Step 2: Find the inverse total demand function, i.e., P as a function of QD.
- Start from QD = 100 − 2P and solve for P: 2P = 100 − QD, so P = 50 − 0.5 QD.
- This shows the coefficient of QD in the inverse function is 0.5, which corresponds to the missing value.

Step 3: Interpret the inverse function format and check consistency.
- The inverse P = 50 − 0.5 QD means as total quantity increases, price falls by 0.5 for each additional unit of QD, which aligns with a downward-sloping demand curve.

Optional check (optional sub-question): evaluate QD at a given price to verify the forward function.
- If P = 50, each individual demand qD = 10 − 0.2(50) = 10 − 10 = 0, so total QD = 10 * 0 = 0.
- Plugging QD = 0 into the inverse: P = 50 − 0.5(0) = 50, which matches the price used in the forward calculation.

Thus, the missing coefficient in the inverse demand function is 0.5, and the total demand function is QD = 100 − 2P. If you’re asked to compute QD at a specific price like P = 50, you’ll get QD = 0.00 when rounded to two decimals.

ECON 302 AL1 SP25: Inter Microeconomic Theory (Buckley, B)

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