https://file.aiquickdraw.com/mathbot/file/1727171426396ivspn49x.jpg

It looks like you've uploaded a set of practice questions. Let's go through them step by step. I'll address the first set of questions.

### Question 4:

**Given:**
- When the price of a product is Rp 500, the demand is 1,500 units.
- When the price increases to Rp 600, the demand decreases to 1,200 units.

We are asked to:

a) **Find the equation of the demand function:**

We assume a linear demand function of the form:
\[
Q = mP + b
\]
Where:
- \(Q\) = quantity demanded
- \(P\) = price

We are given two points:
- \(P = 500, Q = 1500\)
- \(P = 600, Q = 1200\)

First, we find the slope \(m\) using the formula for the slope between two points:
\[
m = \frac{Q_2 - Q_1}{P_2 - P_1} = \frac{1200 - 1500}{600 - 500} = \frac{-300}{100} = -3
\]

Now, using the point-slope form, we substitute one point (e.g., \(P = 500\), \(Q = 1500\)) into the equation:
\[
Q - 1500 = -3(P - 500)
\]
Expanding and solving for \(Q\):
\[
Q = -3P + 3000
\]

Thus, the equation of the demand function is:
\[
Q = -3P + 3000
\]

b) **Draw the curve:**

This would be a straight line with slope -3 and y-intercept 3000 on a graph with price (P) on the x-axis and quantity (Q) on the y-axis. The line crosses the y-axis at 3000 and decreases with a slope of -3.

c) **What is the highest price that consumers can afford?**

The highest price consumers can afford is when the quantity demanded \(Q = 0\). Set \(Q = 0\) in the equation and solve for \(P\):
\[
0 = -3P + 3000
\]
\[
P = 1000
\]

So, the highest price is **Rp 1000**.

d) **If a customer purchases 300 units, what is the price?**

Substitute \(Q = 300\) into the demand equation and solve for \(P\):
\[
300 = -3P + 3000
\]
\[
3P = 2700
\]
\[
P = 900
\]

So, the price is **Rp 900**.

---

Do you need a detailed explanation for the next set of questions? Here's a list of follow-up questions to explore:

1. How do we adjust the equation if the relationship between price and demand is nonlinear?
2. Can this same approach be applied to supply functions?
3. How would the graph change if the slope were steeper or less steep?
4. What external factors might cause the demand curve to shift?
5. What happens if a price ceiling is introduced in the market?

**Tip:** Always verify units when interpreting supply and demand equations to ensure they make sense in context.

If the price of a product is Rp 500, then consumers will buy 1,500 units of the product, but if the price increases to Rp 600, then consumers will only buy 1,200 units. What is the equation of the function? What is the highest price consumers can afford?

Solve a linear demand function using two given points, where the price of a product changes and consumers' quantity demanded also shifts. Learn how to find the equation of the demand function and determine the highest price consumers are willing to pay.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation