(Please show all of your work - no shortcuts): The short-run total cost equation
ID: 1103765 • Letter: #
Question
(Please show all of your work - no shortcuts): The short-run total cost equation for a firm in the raspberry jam industry has been estimated to be:
TC = 9025 + 0.01q2
where q is the number of cases of jam produced by this firm in a year and costs are measured in dollars per year.
where q is the number of cases of jam produced by this firm in a year and costs are measured in dollars per year.
What are the annual fixed costs for this firm?
What is the equation for average total cost? What is the equation for average variable cost?
Marginal cost in this case is given by: MC = 0.02q. Provide a rough sketch of the average total cost curve and the marginal cost curve. (Suggestion: It will be easier to draw the ATC curve if you start with a relatively large q, say q = 500, rather than a q near zero.) At what output level do they intersect? What is the value of average total cost at this output level?
Explanation / Answer
1. FC = 9025
2. ATC = TC/Q = 9025/Q + 0.01Q
3. AVC = TVC/Q = 0.01Q
4. MC cuts ATC at its minimum
Min ATC = dATC/dQ = 0
-9025/Q2 + 0.01 = 0
Q2 = 902500
Q = 950 units
5. ATC at Q = 950 will be : 9025/950 + 0.01(950) = $19
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