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Steps to finding the optimal output and price levels

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Company A seeks help with its pricing decision. It has learned that the quantity demanded decreases by 3% when price increases by 1%, demand is constant, and the average quantity and price are the denominators in the percentage changes. Company A knows that marginal cost is constant as output changes but does not know its value. Its current output, price, and total cost are 485, $2,020, and $500,000, respectively. Total cost increases to $566,000 if output increases to 535.
a. What is the price elasticity of demand?
b. What is marginal cost?
c. What is profit when price is $2,020?
d. If elasticity is constant, what price maximizes profit?
e. What is the percentage change in price if price goes from $2,020 to the profit maximizing price? Use the midpoints formula. (See attachment) The attachment identifies the percentage change in price according to the midpoints formula for any price you enter.
f. If the elasticity is constant, what percentage change in quantity occurs if price goes from $2,020 to the profit maximizing price?
g. What is the profit maximizing quantity if elasticity is constant? The attachment identifies the percentage change in quantity according to the midpoints formula for any quantity you enter.
h. What is the maximum profit?
i. If average total cost does not change when output increases to 535, what price maximizes profit?

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a. What is the price elasticity of demand?
Percent change in quantity demanded=-3%
Percent change in price=+1%
Price elasticity of demand=Percent change in quantity demanded/Percent change in price
=(-3%)/(+1%)=-3

b. What is marginal cost?
Total cost at output of 485=$500,000
Total cost at output of 535=$566,000
Marginal Cost=Change in total cost/Change in output=(566000-500000)/(535-485)=$1320

c. What is profit when price is $2,020?
Total ...

Solution Summary

The solution depicts the steps to estimate optimal price and output levels.

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Finding optimal output and price levels problem

Please help with the following economics problem. Provide step by step calculations.

You are the manager of a firm that sells its product in a competitive market at a price of 50. Your firms cost structure is c=40 + 5Q2.

The profit maximizing output for your firm is one of the following:

4/5
10
5
45

Suppose a monopolistic knows the own-price elasticity of demand for its product is -3 and its marginal cost of production is constant MC(Q) = 10. To maximize its profits, the monopoly price is

1.50 per unit
6.67 per unit
10.00 per unit
15.00 per unit

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