It costs a company $20,000 to begin production of a good, plus $4 for every unit

Question

It costs a company $20,000 to begin production of a good, plus $4 for every unit of the good produced. Let x be the number of units produced by the company.

(a) Find a formula for C(x), the total cost for the production of x units of the good.

(b) Find a formula for the company's average cost per unit, a(x).

(c) knowing that the graph of y = a(x) for 0 < x ? 50,000, 0 ? y ? 10. is the following:

(i) Explain in economic terms why the graph of a has the long-run behavior that it does.

(ii) Explain in economic terms why the graph of a has the vertical asymptote that it does.

Explanation / Answer

(a) C(x) = 20000 + 4x

This would be the total cost function where 20000 is teh fixed cost and 4 is teh varaiable cost.

(b) Average cost =Total cost / no f units

C(x) / x = 20000/x + 4

(c) y = a(x).

Cost y is dependent on x output.

(i) The shape of long run cost explains that with increasing output the cost falls and becomes constant over a range of output. This range forms economies of scale.

(ii) Vertical asymptote here denotes constant cost even when the production is zero.

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