4. Suppose that the inverse demand function for movies is p = 120 – Q1 for college students and p = 120 – 2Q2 for other town residents. What is the town’s total demand function (Q = Q1 + Q2 as a function of p)?
The total demand function for the town is the sum of the demand functions for the two groups.
Let suppose that "P=100". Then, from the first and second demand functions we get:
Therefore, "Q=Q_1+Q_2=20+10=30."
Then, let's do the same calculations for "P=60":
As we can see from calculations, we obtain two points on total demand curve: ("x_1", "y_1") and ("x_2", "y_2") or (30, 100) and (90, 60), respectively. Let's use the point slope formula to find the total demand function:
here, "y=P", "y_1=100", "x=Q", "x_1=30", "m" is the slope of the line.
So, we can rewrite the equation:
The slope of the line can be found as follows:
Then, substituting the slope into the equation of the line, we get:
Answer:
"P=120-0.67Q."
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