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.)

Question

BlackTom AI · Accepted Answer

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)

View Explanation

Log in for full answers

Similar Questions

The image above shows which demand curve?

Suppose the demand equation for a product is given by: Qd = 50 - 12\frac{1}{2}P b) Calculate the price at which consumers would demand 10 units of the product. Price: $ [Fill in the blank],

Suppose that a consumer had a utility function given by: U=X2Y4. This consumer has a budget of $12.Fill in the value of this consumer's demand function. X = Answer Question 3[input](1/Px).(For instance, if X = 4/Px, then X = 4 (1/Px) and enter 4)

Suppose the demand function for Good X was given by: QDx = 58 - 4Px.Calculate the reservation price for the 38th unit.(Do not include a $ sign in your response.)

Suppose the demand for a good was given by the function: QD = 230 - 0.1 P.Calculate the choke price of this demand function.(Do not include a $ sign in your response.)

The demand function for this good is given by: QD= 225 -0.5P. Find quantity demanded when price is $300.

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler