Use the function below (whose parameters qualify it as a STC function) to answer the questions. See the text p. 244 for a representative figure. STC = 600 + 100Q - 7Q2 + .2Q3 a. Find the value of Q at which AVC is a minimum. b. Is productive efficiency at this value greatest or least? c. Demonstrate that the value of SMC equals the value of AVC at the value of Q where AVC is a minimum. Hint: The level of Q you found in (f) is where AVC is a minimum. If you plug this level of Q into AVC (see c) and also into MC (see d) the two outcomes should be the same if SMC crosses AVC at this level of Q. d.Why does the derivative of Short Run Total Cost (STC) equal the derivative of Total Variable Cost (TVC)? Stated another way, why does dSTC/dQ = dTVC/dQ? Explain in a couple of sentences (Hint: See Truett page 235 and footnote 16). e. Find the value of Q where increasing returns ceases and diminishing returns begins. Hint: Diminishing returns begins at the level of Q where MC is a minimum
Use the function below (whose parameters qualify it as a STC function) to answer the questions. See the text p. 244 for a representative figure.
STC = 600 + 100Q - 7Q2 + .2Q3
a. Find the value of Q at which
b. Is productive efficiency at this value greatest or least?
c. Demonstrate that the value of SMC equals the value of AVC at the value of Q where AVC is a minimum. Hint: The level of Q you found in (f) is where AVC is a minimum. If you plug this level of Q into AVC (see c) and also into MC (see d) the two outcomes should be the same if SMC crosses AVC at this level of Q.
d.Why does the derivative of Short Run Total Cost (STC) equal the derivative of Total Variable Cost (TVC)? Stated another way, why does dSTC/dQ = dTVC/dQ? Explain in a couple of sentences (Hint: See Truett page 235 and footnote 16).
e. Find the value of Q where increasing returns ceases and diminishing returns begins. Hint: Diminishing returns begins at the level of Q where MC is a minimum.
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