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# Inverse Demand function

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Consider a manufacturer with two factories. They can produce at either factory or both. However, we need to consider the quantities that will be produced at each factory. The firm can sell its products in Milwaukee and Madison.

The firms production cost is C= .5q2 +500 where q is the number of items produced.
If the firm sells its products in Milwaukee, the transportation cost is zero. However, if it sells its products in Madison, the transportation cost is \$6 per item.

The inverse demand function in Milwaukee is p(q) = 60 - qMilwaukee
Madison is a competitive market where p=\$30

a. How many items (q) will the firm sell in Milwaukee?
b. What is the Marginal Revenue in Milwaukee?
c. What is the Price in Milwaukee?
d. What is the firmâ??s total profit?
e. Is this a case of First, Second, or Third Degree Price Discrimination?

https://brainmass.com/economics/production-function/inverse-demand-function-326246

#### Solution Preview

a. How many items (q) will the firm sell in Milwaukee?

Total profit = rev. in Milwaukee + rev. in Madison - total cost
Let Qmil be the quantity sold in Milwaukee, Qmad be ...

#### Solution Summary

Inverse Demand function

\$2.19