Answer to Question #63772 in Other Economics for hamza
a. ATC = TC/Q = 100/Q + 8 – 0.12Q + 0.004Q2,
AVC = VC/Q = 8 – 0.12Q + 0.004Q2,
MC = TC' = 8 - 0.24Q + 0.012Q2,
AFC = FC/Q = 100/Q
b. Diminishing returns set in at such level of output, for which MC is minimal or MC' = 0, so:
-0.24 + 0.024Q = 0,
Q = 10 units.
c. AVC is at its minimum, when AVC = MC or AVC' = 0, so:
-0.12 + 0.008Q = 0,
Q = 15 units.
d. MC and AVC equal at the point, where AVC is at its minimum, so Q = 15 units.
e. AVC reaches a minimum before ATC reaches a minimum, because ATC > AVC and MC is increasing.
f. If at the point where the ATC is at minimum, MPL = 12, MPK = 18, w = RM8, then the price of capital per hour k is:
MPL/w = MPK/k,
12/8 = 18/k,
k = 12.
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