022 Exam 1 Sample A, Problem 5

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Find the marginal revenue and marginal profit at , given the demand function

and the cost function

Should the firm produce one more item under these conditions? Justify your answer.

Foundations:  
Recall that the demand function, , relates the price per unit to the number of units sold, .

Moreover, we have several important important functions:

  • , the total cost to produce units;
  • , the total revenue (or gross receipts) from producing units;
  • , the total profit from producing units.
In particular, we have the relations
and
Finally, marginal profit at units is defined to be the effective cost of the next unit produced, and is precisely . Similarly, marginal revenue or cost would be or , respectively.

 Solution:

Step 1:  
Write the Basic Equation:

!Final Answer:   |- |With units, we have that the ladder is sliding down the wall at   feet per second. |}

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