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Price Elasticity of Demand and Inverse Demand Function

4. Given the following cost and inverse demand function

P(Q) = 50 - .00025Q
C(Q) = 361, 250 + 5Q + .0002Q²
a. Find the total revenue?
b. Find the marginal and average costs and graph the functions in the ranges of Q= 40,000, 42500, 45,000.
c. Briefly explain the point of intersection between MC and ATC (AC) in terms of production and cost theory.
d. Calculate the profit maximization level of production (activity) and the total profit earned by the firm.
e. What is/are the breakeven levels of operation (activities)?
f. Calculate the price elasticity of demand at profit maximization level of output?

Solution Preview

Please see the attached file.

P(Q) = 50 - .00025Q
C(Q) = 361,250 + 5Q + .0002Q²
a. Find the total revenue?
TR = PQ = 50Q - 0.00025Q2
b. Find the marginal and average costs and graph the functions in the ranges of Q= 40,000, 42500, 45,000.
MC = dC/dQ = 5 + 0.0004Q
AC = C/Q = 361250/Q + 5 + ...

Solution Summary

The expert calculates the price elasticity of demand at profit maximizing level of output.

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