Introduction to Calculus in Economics (continued): In the previous Problem Set question, we started looking at the cost function C (z), the cost of a firm producing z items. An important microeconomics concept is the marginal cost, defined in (non-mathematical introductory) economics as the cost of producing one additional item (C(2+h)-C(z)) If the current production level is z items with cost C (2), then the cost of computing h additionial items is C (z+h). The average cost of those h items is c' (z) Use this function in the model below for the Marginal Cost function MC(2) As we analyze the cost of just the last item produced, this can be made into a mathematical model by taking the limit as h 0, le. the derivat Problem Set question: The cost, in dollars, of producing z units of a certain item is given by C(z) = 0.02 - 10z + 450 a) Find the marginal cost function MC (z) = (b) Find the marginal cost when 40 units of the item are produced. The marginal cost when 40 units are produced is $ c) Find the actual cost of increasing production from 40 units to 41 units. The actual cost of increasing production from 40 units to 41 units is $
Introduction to Calculus in Economics (continued): In the previous Problem Set question, we started looking at the cost function C (z), the cost of a firm producing z items. An important microeconomics concept is the marginal cost, defined in (non-mathematical introductory) economics as the cost of producing one additional item (C(2+h)-C(z)) If the current production level is z items with cost C (2), then the cost of computing h additionial items is C (z+h). The average cost of those h items is c' (z) Use this function in the model below for the Marginal Cost function MC(2) As we analyze the cost of just the last item produced, this can be made into a mathematical model by taking the limit as h 0, le. the derivat Problem Set question: The cost, in dollars, of producing z units of a certain item is given by C(z) = 0.02 - 10z + 450 a) Find the marginal cost function MC (z) = (b) Find the marginal cost when 40 units of the item are produced. The marginal cost when 40 units are produced is $ c) Find the actual cost of increasing production from 40 units to 41 units. The actual cost of increasing production from 40 units to 41 units is $
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.1P
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This is a calculus class with an introduction to ecenomics and I need help understanding how to evaluate this question.
Transcribed Image Text:Introduction to Calculus in Economics (continued):
In the previous Problem Set question, we started looking at the cost function C (x), the cost of a firm producing z items. An important microeconomics concept is the marginal cost, defined in (non-mathematical introductory) economics as the cost of producing one additional item.
If the current production level is z items with cost C (x), then the cost of computing h additionial items is C (r +h). The average cost of those h items is e ote As we analyze the cost of just the last item produced, this can be made into a mathematical model by taking the limit as h → 0, i.e. the derivative
h
C' (x). Use this function in the model below for the Marginal Cost function MC (x).
Problem Set question:
The cost, in dollars, of producing z units of a certain item is given by
C (2) = 0.02a3 – 10x + 450.
(a) Find the marginal cost function.
MC (x) =
(b) Find the marginal cost when 40 units of the item are produced.
The marginal cost when 40 units are produced is $
(c) Find the actual cost of increasing production from 40 units to 41 units.
The actual cost of increasing production from 40 units to 41 units is $
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