A firm has the following information on production and costs from past data: Output (Y) Total Cost (TC) 0 9 6 2775 12 5361 known known to be 18 8199 If the total cost function is demand for the TC=aY³+bY²+kY+f, and 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.
A firm has the following information on production and costs from past data: Output (Y) Total Cost (TC) 0 9 6 2775 12 5361 known known to be 18 8199 If the total cost function is demand for the TC=aY³+bY²+kY+f, and 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.
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.9P
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Question
Transcribed Image Text:A firm has the following information on production
and costs from past data:
Output
(Y)
6
12
18
Total Cost (TC)
2775
5361
8199
If the
total
cost
function is known
to
be
TC = aY'+ bY² + 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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