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# notes_2150a_Ch8_part+2.docx

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Western University

Economics

Economics 2150A/B

Prof

Fall

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Micro Chapter 8 part 2
Practice problems:
1
8.7 Afirm’s long-run total cost curve is TC(Q)=1000Q 2 . Derive the equation for the
AC(Q).
corresponding long-run average cost curve, Given the equation of the long-run
average cost curve, which of the following statements is true:
a. The long-run marginal cost curve MC(Q) lies below AC(Q) for all positive
quantities Q.
MC(Q) AC(Q)
b. The long-run marginal cost curve is the same as the for all positive
Q.
quantities
MC(Q) AC(Q)
c. The long-run marginal cost curve lies above the for all positive
Q.
quantities
d. The long-run marginal cost curve MC(Q) lies below AC(Q) for some positive
quantities Q and above the AC(Q) for some positive quantities Q.
ANSWER: a
The equation of the AC curve is AC(Q) = TC(Q)/Q = 1000Q /Q = 1000Q -(1/. This is a
decreasing function of Q. Given the relationship between AC and MC curves, the fact that the
AC curve is decreasing means that the MC curve must lie below the AC curve.
8.9. Afirm’s long-run total cost curve is TC(Q) = 40Q − 10Q + Q , and its long-run
2
marginal cost curve is MC(Q) = 40 − 20Q + 3Q . Over what range of output does the
production function exhibit economies of scale, and over what range does it exhibit
diseconomies of scale?
2
AC(Q) = 40−10Q+Q
From the total cost curve, we can derive the average cost curve, . The
minimum point of theAC curve will be the point at which it intersects the marginal cost curve,
2 2
40−10Q+Q = 40−20Q+3Q
i.e. . This implies that AC is minimized when Q = 5. By
definition, there are economies of scale when the AC curve is decreasing (i.e. Q < 5) and
diseconomies when it is rising (Q > 5). 8.10. For each of the total cost functions, write the expressions for the total fixed cost,
average variable cost, and marginal cost (if not given), and draw the average total cost and
marginal cost curves.
a) TC(Q) = 10Q
b) TC(Q) = 160 + 10Q
2
c) TC(Q) = 10Q , where MC(Q) = 20Q
d) TC(Q) = 10√Q, where MC(Q) = 5/√Q
e) TC(Q) = 160 + 10Q , where MC(Q) = 20Q
a) TFC = 0, AVC = 10, MC = 10.
MC = AC = 10
b) TFC = 160, AVC = 10, MC = 10.
AC
MC = 10 c) TFC = 0, AVC = 10Q.
MC
AC
10 Q
d) TFC = 0, AVC = . AC
MC
e) TFC = 160, AVC = 10Q.
MC
AC 8.11. Afirm produces a product with labor and capital as inputs. The production function
is described by Q = LK. The marginal products associated with this production function are
MP = K and MP = L. Let w = 1 and r = 1 be the prices of labor and capital, respectively.
L K
a) Find the equation for the firm’s long-run total cost curve as a function of quantity Q.
b) Solve the firm’s short-run cost-minimization problem when capital is fixed at a quantity
of 5 units (i.e., K = 5). Derive the equation for the firm’s short-run total cost curve as a
function of quantity Q and graph it together with the long-run total cost curve.
a) Cost-minimizing quantities of inputs are equal to L = √Q √(r/w) and K = √Q / √(r/w).
Hence, in the long-run the total cost of producing Q units of output is equal to TC(Q) = 10 +
2√(Qrw). For w = 1 and r = 1 we have TC(Q) = 2√Q.
b) When capital is fixed at a quantity of 5 units (i.e., K = 5) we have Q = K L = 5 L. Hence,
in the short-run the total cost of producing Q units of output is equal to STC(Q) = 5 + Q/5.
8.14. Consider a production function of two inputs, labor and capital, given by Q = (√L +
√K) . The marginal products associated with this production function are as follows:
Let w = 2 and r = 1.
a) Suppo

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