Math Problem Statement
Solution
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: Where:
- = quantity demanded
- = price
We are given two points:
First, we find the slope using the formula for the slope between two points:
Now, using the point-slope form, we substitute one point (e.g., , ) into the equation: Expanding and solving for :
Thus, the equation of the demand function is:
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 . Set in the equation and solve for :
So, the highest price is Rp 1000.
d) If a customer purchases 300 units, what is the price?
Substitute into the demand equation and solve for :
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:
- How do we adjust the equation if the relationship between price and demand is nonlinear?
- Can this same approach be applied to supply functions?
- How would the graph change if the slope were steeper or less steep?
- What external factors might cause the demand curve to shift?
- 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.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Demand Function
Formulas
Slope formula: m = (Q2 - Q1) / (P2 - P1)
Point-Slope Form: Q - Q1 = m(P - P1)
Theorems
Linear Function
Suitable Grade Level
High School Economics or Mathematics
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