if the demand function is p=10 10 -3q and the average cost is AC =q then what will be the output in equilibrium condition?
Answers
Answer:
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Explanation:
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Answer:
Q = 10 must be a maximum.
Explanation:
CALCULUS APPROACH
Revenue = PQ
So, we have
Revenue = -5Q^2 + 100Q
The derivative of Revenue with respect to Q is
MR = Marginal Revenue = -10Q + 100
Setting this to 0 yields Q = 10.
We know that this is a maximum because the derivative of Marginal Revenue is
D(MR) = -10 < 0
Putting Q = 10 into the Revenue function shows that the Maximum Revenue = 500.
QUADRATIC REVENUE EQUATION APPROACH
You really don’t need calculus to solve this problem.
Revenue is a quadratic function, and so its curve is a parabola. Let the equation be …
Revenue = aQ^2 + bQ + c
The middle of the parabola is Q = -b/2a. In this case, the midpoint is Q = -100/(-5 x 2) = 10. This is either a maximum or minimum point of the parabola.
When Q = 10 in the Revenue function, we get Revenue = 500. When Q = 0 (another point on the parabola), Revenue = 0 (as should be expected).
So, Q = 10 must be a maximum.
GRAPHICAL APPROACH
Just draw a graph for Revenue starting with Q = 0 and going upwards. Then, read the answer off the graph.
Q = x axis
Revenue = y axis
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