Question

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

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

1. Total fixed cost is $_________

2. Obtain the AFC function from (a) and write it here _____________

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

4. Write here the MC function __________________________

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

Also write a sentence or two explaining what this implies for fixed costs per unit (AFC) as production quantities get ever larger.

6. 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.   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.

Answer 1

(a)

Total fixed cost (TFC) = 400 (since fixed cost is independent of output)

(b)

Average fixed cost (AFC) = TFC/Q = 400 / Q

(c)

Total variable cost (TVC) = 50Q - 5Q² + 2Q³ (since TVC depends on and varies with Q)

AVC = TVC/Q = 50 - 5Q + 2Q²

(d)

MC = dSTC/dQ = 50 - 10Q + 6Q²

(e)

When Q is very large, (400 / Q) becomes very small and therefore, AFC tends to zero.

This means that when output becomes very high, all costs become variable since fixed costs tend to zero.

(f)

AVC is minimum when dAVC/dQ = 0.

dAVC/dQ = - 5 + 4Q = 0

4Q = 5

Q = 1.25

NOTE: As per Answering Policy, 1st 6 parts are answered.