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Eco 615 Problem Set 1

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Mathematics
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uc riverside
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Problem Set 1
1) In the Woolverton/Manteca example, at what prices are tickets sold to each group? Why
do you think the prices are different?
2) Suppose a firm sells its output for
 

Where Q is the quantity it produces and sells. Total costs is given by
   
What is the profit maximizing value for production? At what price is this product sold
for? Use the MR=MC approach at the end of the question.





 


 
 

The profit maximization quantity is 16,000 and the price for this product is $4.
3)
In the above figure, you see the marginal revenue and marginal cost functions for a firm with a
single output. Assume that both total revenue and total cost equal zero when Q = 0. Where do

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you think the profit maximizing level of production for the firm will be? Explain with the help
of a diagram.
  
Profit = TR- TC
The maximization of profit is possible when the vertical distance between TR and TC is
greatest. Because the value of TR and TC is zero when the quantity is 0 the curves start at Q= 0
The profit maximization will be at the point where the marginal revenue (MR) is greater than the
marginal cost (MC).
4) I claimed in class that the problem in our luxury box example was that price was lowered
too much in order to obtain 1 extra seat sale
Note
 

 
a. Compute the percentage change in price and the percentage change in quantity demanded
when price falls from $1,000,000 to $950,000 and the boxes increase from 25 to 26.

 

 

 

 
b. What is the Elasticity of Demand for luxury boxes?


 
c. At what new lower price will total revenue be unchanged?

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Problem Set 1 1) In the Woolverton/Manteca example, at what prices are tickets sold to each group? Why do you think the prices are different? 2) Suppose a firm sells its output for 𝑃 = 20 − 𝑄 1000 Where Q is the quantity it produces and sells. Total costs is given by 𝑇𝐶 = 5000 + 4𝑄 What is the profit maximizing value for production? At what price is this product sold for? Use the MR=MC approach at the end of the question. 𝑑 𝑀𝐶 = 𝑑𝑄 (𝑇𝐶) 𝑑 𝑀𝐶 = (500 + 4𝑄) 𝑑𝑄 𝑀𝐶 = 4 𝑃 = 𝑀𝐶 = 4 4 = 20 − 0.001𝑄 −16 = −0.001𝑄 𝑄 = 16,000 The profit maximization quantity is 16,000 and the price for this product is $4. 3) In the above figure, you see the marginal revenue and marginal cost functions for a firm with a single output. Assume that both total revenue and total cost equal zero when Q = 0. Where do you think the p ...
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