Math 157 Calculus Class Notes

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Chapter 4.1 Marginal Functions in Economics
___________ Cost: Suppose that C ( x ) describes the cost function for producing x number of a certain product. Then the ___________ cost is the derivative of the cost function, C ( x) , and measures the rate of ________ of the cost function ______________ the number of units ______________. Note 1: The marginal cost for a particular value of x is the ___________ cost of one __________ unit of production. ___________ Revenue Function: R( x)  px  xf ( x) , where p  f ( x) is the unit ________ function and x the __________ of units sold. Note 2: The unit price function comes from solving the ___________ equation in x and p for ____. ___________ Revenue: Suppose that R( x ) describes the revenue function for selling x number of a certain product. Then the ___________ revenue is the derivative of the revenue function, R( x) , and measures the rate of ________ of the revenue function ______________ the number of units ______________.

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Note 3: R( x) 

d xf ( x)  dx

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Note 4: The marginal revenue for a particular value of x is the ___________ revenue of one __________ unit sold. ___________ Profit: Suppose that P( x ) describes the profit function for producing and selling x number of a certain product. Then the ___________ profit is the derivative of the profit function, P( x) , and measures the rate of ________ of the profit function ______________ the number of units ______________ and ______________. Note 5: The marginal profit for a particular value of x is the ___________ profit of one ___________ unit of production. ___________ Cost Function: Suppose C ( x ) is a total cost function. Then the ___________ cost function, denoted by C ( x ) , is C ( x)  Note 6: C ( x ) is read C bar of x. Note 7: Similarly, ___________ revenue and ___________ profit are defined. .

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___________ Average Cost: Suppose that C ( x ) describes the cost function for producing x number of a certain product.