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Equations for Fixed, Variable, Average and Marginal Costs

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5. Given TC = 100 + 50Q - 12 Q² + Q³ where TC is total cost and Q is output,

a. What are the equations for total fixed cost, total variable cost, average fixed cost, average variable cost and marginal cost?
b. Where is the point of diminishing marginal returns?
c. Where does stage II of the production function begin?
d. Show that MC = AVC when AVC is at a minimum.

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The expert examines the equations for fixed, variable, average and marginal costs.

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Fixed costs are the costs that are independent of the number of goods you produce, or more simply the costs you incur when you do not produce any goods. So we substitute in Q = 0 to our equation and we get 100 + 50*0 -12*0 +0 = 100. So our fixed cost of production is 100.

Total Variable Costs = Total Costs - Fixed Costs. In this case, we have (100 + 50*Q -12*Q^2 +Q^3) -100 = 50*Q -12*Q^2 +Q^3. We can calculate our total variable costs at a ...

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