A firm has the following information on production and costs from past data: Output (Y) 0 6 12 18 Total Cost (TC) 9 2775 5361 8199 If the total cost function is known to be TC = aY³ + by²+kY+f, and the demand for the product of the firm is Y-320-(1/2). P answer the following: Determine the coefficients of the cubic cost function. Derive all cost and revenue curves and the profit function. Show that the MC cuts the AVC when AVC is at its minimum point. Plot the relevant graph indicating all points.

A firm has the following information on production and costs from past data: Output (Y) 0 6 12 18 Total Cost (TC) 9 2775 5361 8199 If the total cost function is known to be TC = aY³ + by²+kY+f, and the demand for the product of the firm is Y-320-(1/2). P answer the following: Determine the coefficients of the cubic cost function. Derive all cost and revenue curves and the profit function. Show that the MC cuts the AVC when AVC is at its minimum point. Plot the relevant graph indicating all points.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

A firm has the following information on production
and costs from past data:
Output
(Y) 0
12
18
6
Total Cost (TC)
9
2775
5361
8199
If the
total
cost
function is known
to
be
TC = aY' + bY ² + kY + ƒ , and the demand for the
product of the firm is Y = 320-(1/2). P answer the
following:
• Determine the coefficients of the cubic cost function.
• Derive all cost and revenue curves and the profit
function.
Show that the MC cuts the AVC when AVC is at its
minimum point. Plot the relevant graph indicating all
points.
Calculate the break even and profit maximizing levels of
output and price.
• What is the relationship between price, marginal revenue
and own price elasticity of demand at the profit
maximization point.

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Step 1: Define cost

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Step 3: Derive cost, revenue and profit functions

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Step 4: Graph the MC and AVC curves

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