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Types of cost curves, mathematically. (10 points) Suppose that a coffee producer’s total cost function is T C(Q) = 288 + 3Q + 2Q2 . (a) (3 points) Find the expressions for the average total cost (AT...

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Types of cost curves, mathematically. (10 points) Suppose that a coffee producer’s total cost function is T C(Q) = 288 + 3Q + 2Q2 . (a) (3 points) Find the expressions for the average total cost (AT C(Q)), the average variable cost (AV C(Q)), and the marginal cost (MC(Q)). (b) (3 points) At what quantity is the average total cost minimized? (c) (4 points) Does this production function exhibit economies of scale, diseconomies of scale, or constant economies of scale? If it is different at different levels of output, then you should state the values of Q associated with each.
Answered Same Day Dec 25, 2021

Solution

Robert answered on Dec 25 2021
130 Votes
The given total cost function is given below.
TC(Q) = 288 + 3Q + 2Q
2

a) Average total cost function or ATC (Q) = TC(Q)/Q = (288 + 3Q + 2Q2)/Q = (288/Q) + 3 +
2Q
Marginal cost function or MC(Q) = dTC/dQ = 3+ 4Q
Average variable cost function or AVC(Q) = VC(Q)/Q = (3Q+2Q
2
)/Q = 3 +...
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