Question

Love Econ shoes factory has the total cost function of 𝑇𝐶(𝑠)=500+3𝑠+5𝑠2.

Please complete the following:

(a) Total Variable Costs:

(b) Total Fixed Costs:

(c) Average Variable Costs:

(d) Average Fixed Cost:

(e) Average Total Costs:

(f) Marginal Costs:

(g) At what amount of output is average total cost minimized?

(h) Draw total fixed cost curve when Love is producing 300,000 units of shoes.

Answer 1

Total Cost Function:

$TC = 500 + 3s + 5 s\\^2$

(a) Total Variable Costs:

 Fixed Costs= 500

Total variable cost includes only the variable component of the total cost.

Total Variable Costs: $3s + 5 s\\^2$

(b) Total Fixed Costs:

 Total fixed cost includes only the fixed parts of the total cost that does not change with the level of output.

Total Fixed Costs = 500

(c) Average Variable Costs: $\frac{Total\ Variable\ Costs}{s}$

$=\frac{3s + 5 s\\^2}{s}$

= $=3 + 5s$

(d) Average Fixed Cost:

$=\frac{Total\ Fixed\ Costs}{s}\\ =\frac{500}{s}$

(e) Average Total Costs:

Average Total Costs = $=\frac{Total\ Costs}{s}\\ \\ \frac{500 + 3s + 5 s\\^2}{s}\\ \frac{500 }{s} + 3 + 5s$

(f) Marginal Costs:

Marginal Costs = $\frac{dTotalCost}{ds}\ = 3 + 10s$

(g) At what amount of output is average total cost minimized?

Differentiating the average total cost with respect to s and equating it to 0 -

$\frac{-500}{s\\^2} + 5 = 0\\ s = 10$

Hence, output level = 10 the average total cost is minimized.

(h) Draw total fixed cost curve when Love is producing 300,000 units of shoes.