A. To find the expressions for AVC, AFC, and MC, we need to first find the expressions for average variable cost (AVC), average fixed cost (AFC), and marginal cost (MC).
1. Average variable cost (AVC):
AVC = TVC / Q
Where TVC is the total variable cost.
In this case, the total variable cost can be found by subtracting the total fixed cost (TFC) from the total cost (TC).
TVC = TC - TFC = 100 + 60Q + 4Q^2 - TFC
2. Average fixed cost (AFC):
AFC = TFC / Q
3. Marginal cost (MC):
MC = ΔTC / ΔQ
Where ΔTC is the change in total cost and ΔQ is the change in quantity.
B. To find the levels of output that minimize AVC and MC, we need to take the derivative of both expressions with respect to Q and set it equal to zero.
1. To minimize AVC:
Take the derivative of AVC with respect to Q and set it equal to zero:
d(AVC)/dQ = (d(TVC)/dQ) / Q - TVC / Q^2 = 0
Solve for Q that satisfies this equation.
2. To minimize MC:
Take the derivative of MC with respect to Q and set it equal to zero:
d(MC)/dQ = (d(TC)/dQ) / Q - TC / Q^2 = 0
Solve for Q that satisfies this equation.
C. To find the minimum values of MC and AVC, substitute the values of Q obtained from part B into the expressions for MC and AVC, and calculate their respective values.
Suppose the short-run cost function of the firm is by: TC = 100 + 60Q + 4Q^2. Find:
A. The expression of AVC, AFC and MC
B. The levels of output, that minimize AVC and MC
C. The minimum values of MC and AVC
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