Question

The total cost curve of a firm is given by TC=Q³-12Q²+50Q+100. A. Determine total fixed cost function, total variable cost function, average total cost function, average variable cost function and marginal cost function B.calculate total cost,average total cost,average variable cost and marginal cost when the firm produces 20 units of output. C.calculate the level of output at which marginal cost is minimum

Answer 1

A.

$$FC=100$$

$$VC=Q^3-12Q^2+50Q$$

$$ATC=Q^2-12Q+50+\frac{100}{Q}$$

$$AVC=Q^2-12Q+50$$

$$MC=3Q^2-24Q+50$$

B.

$$TC\vert_{Q=20}=4300$$

$$VC\vert_{Q=20}=4200$$

$$AVC\vert_{Q=20}=210$$

$$MC\vert_{Q=20}=770$$

C.

$$3Q^2-24Q+50=0$$

$$24^2-4\times3\times50=-24$$