SHORT RUN COSTS

Use the function below (whose parameters qualify it as a STC function) to answer the questions.

STC = 400 + 50Q -5Q^2 + 2Q^3

a.Total fixed cost is $_________

b.Obtain the AFC function from (a) and write it here_____________

c.Obtain the AVC function contained in the STC function and write the AVC function here _________________________

d.Write here the MC function __________________________

e.Find the value which AFC approaches as Q gets very large.

Explain what this implies for fixed costs per unit (AFC) as production quantities get ever larger.

f.Find the value of Q at which AVC is a minimum.

g.Is productive efficiency at the value in (f) greatest or least?

h.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.

i.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).

j.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.