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Price Elasticity of Demand and Inverse Demand Function

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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?

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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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See Also This Related BrainMass Solution

Inverse, Direct Demand Function, & Point Price Elasticity

Inverse, Direct Demand Function, & Point Price Elasticity

Copy and paste the following data into Excel:
a) Run OLS to determine the inverse demand function (P = f(Q)); how much confidence do you have in this estimated equation? Use algebra to then find the direct demand function (Q = f(P)).
b) What is the point price elasticity of demand when P=$42? How would you characterize demand when the price is around $42?
c) What is the point price elasticity of demand when P=$24? How would you characterize demand when the price is around $24?
d) To maximize total revenue, what would you recommend if the company was currently charging P=$42? If it was charging P=$24?
e) Determine an equation for MR as a function of Q, and create a graph of P and MR on the vertical and Q on the horizontal axis.
P Q
$44 642
$42 1,108
$26 2,932
$24 3,465
$15 4,007
$10 4,821.

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