Marginal analysis can be daunting because the problems have a few steps. But there are a few basic relationships you can use.

Revenue = Price * Quantity

Profit = Revenue – Cost

To estimate any marginal function, take its derivative. Here are a few examples from class.

**Problem 1** Suppose the demand function is given by *D(Q)* = -0.05*Q* + 100 dollars per unit where *Q* is the number of units demanded by consumers.

- Find and interpret the marginal revenue at
*Q*= 700 units. - If the cost function is given by
*C(Q)*= 9*Q*+ 5650 dollars, find and interpret the marginal profit at*Q*= 700.

This tells us that the 701st unit increases the revenue by $30.

The 701st unit increases profit by $21.

**Problem 2** Suppose the demand function is given by *D(Q)* = -0.01*Q* + 80 dollars per unit where *Q* is the number of units demanded by consumers.

- Find and interpret the marginal revenue at
*Q*= 5000 units. - If the cost function is given by
*C(Q)*= 15*Q*= 50000 dollars, find and interpret the marginal profit at*Q*= 5000.

The 5001st unit decreases revenue by $20.

The 5001st units decreases profit by $35.