Chap3_Economics

# Chap3_Economics - ECONOMICS Example 8 Suppose C(x is the...

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ECONOMICS Suppose C ( x ) is the total cost that a company incurs in producing x units of a certain commodity. The function C is called a cost function. Example 8

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If the number of items produced is increased from x 1 to x 2 , then the additional cost is C = C ( x 2 ) - C ( x 1 ) and the average rate of change of the cost is: 2 1 1 1 2 1 ( ) ( ) ( ) ( ) C x C x C x x C x C x x x x - +Δ - Δ = = Δ - Δ AVERAGE RATE Example 8
The limit of this quantity as x 0, that is, the instantaneous rate of change of cost with respect to the number of items produced, is called the marginal cost by economists: 0 marginal cost = lim x C dC x dx Δ → Δ = Δ MARGINAL COST Example 8

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As x often takes on only integer values, it may not make literal sense to let x approach 0. s However, we can always replace C ( x ) by a smooth approximating function—as in Example 6. ECONOMICS Example 8
Taking x = 1 and n large (so that x is small compared to n ), we have: C ’( n ) C ( n + 1) –

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Chap3_Economics - ECONOMICS Example 8 Suppose C(x is the...

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