. It is known that the number of concert tickets demanded is 150 when the price is €40 and 100 when the price is €60.
(a)Determine the equation of the demand function in the form Q = f(P) and plot the graph of the function.
(b)Use the equation to calculate the change in demand when the price (i) increases by €10, (ii) decreases by €8.


The graph above shows the demand function \( Q = -2.5P + 250 \). The red points indicate the given data points: (40, 150) and (60, 100).

### (b) Calculating Change in Demand

Using the demand function \( Q = -2.5P + 250 \), let's calculate the change in demand for the specified price changes.

**(i) Increase in price by €10**

Let the initial price be \( P = P_0 \). After increasing by €10, the new price is \( P_1 = P_0 + 10 \).

Change in demand:

\[
\Delta Q = Q(P_1) - Q(P_0) = [-2.5(P_0 + 10) + 250] - [-2.5P_0 + 250] = -2.5 \times 10 = -25
\]

So, the demand decreases by 25 units when the price increases by €10.

**(ii) Decrease in price by €8**

Let the initial price be \( P = P_0 \). After decreasing by €8, the new price is \( P_1 = P_0 - 8 \).

Change in demand:

\[
\Delta Q = Q(P_1) - Q(P_0) = [-2.5(P_0 - 8) + 250] - [-2.5P_0 + 250] = -2.5 \times (-8) = 20
\]

So, the demand increases by 20 units when the price decreases by €8.

Would you like any further details, or do you have any questions?

### Related Questions:
1. How does the slope of the demand function affect the elasticity of demand?
2. What is the demand when the price is €0?
3. What would happen to the demand if the price increases to €80?
4. How would the demand function change if a fixed cost is introduced?
5. What are the limitations of using a linear demand function?

**Tip:** When analyzing demand functions, always consider both the price elasticity and external factors that may influence consumer behavior!

It is known that the number of concert tickets demanded is 150 when the price is €40 and 100 when the price is €60. (a) Determine the equation of the demand function in the form Q = f(P) and plot the graph of the function. (b) Use the equation to calculate the change in demand when the price (i) increases by €10, (ii) decreases by €8.

Solve a demand function problem where the number of concert tickets demanded is given at different prices. Learn how to calculate the demand equation Q = -2.5P + 250 and determine the change in demand when prices increase or decrease. Suitable for students in Grades 9-12.

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