Question

Using the below data calculate the quadratic formula.

Then calculate the following:

i) Fixed cost

ii) Average total cost

iii) Marginal cost

d) Using your answers from part c) calculate fixed cost, average total cost, and marginal cost if 25 units

	Coefficient	Std. Error	t-ratio	p-value
const	2.22486	2.29906	0.9677	0.3347
q	0.00434763	0.000230941	18.83	<0.0001
sq_q	1.63160e-08	2.79915e-09	5.829	<0.0001

Answer 1

The quadratic equation is as follows:

C = a + bq + cq²

where C = Cost

a = intercept term(or constant)

b = Coefficient of variable 'q'

c = coefficient of variable 'q²'

Solving the coefficient for variable q² we get,

Coefficient Value = .0000000163

Substituting the values of coefficient gives the cost equation as:

C = 2.22486 + 0.00434763q + 0.0000000163q²

Fixed cost is the cost that is independent of level of output, here it is

Fixed cost = 2.22486

Average total cost = ( Total cost ÷ Output )

Average total cost :

= ( 2.22486 + 0.00434763q + 0.0000000163q²)÷ q

= 2.22486/q + 0.00434763 + 0.0000000163q

Marginal Cost:

Marginal cost = d(Total cost)/d(q)

= 0.00434763 + 2(0.0000000163)q

= 0.00434763 + 0.0000000326q

As it is given that output = q = 25

Substituting the value of q in each of above equations to calculate Average , marginal and fixed cost.

As fixed cost is a constant and here in this equation it is equal to 2.22486 units.

Average total cost :

= (2.22486 + 0.00434763(25) + 0.0000000163(25)²)/25

= 0.09 units

Marginal cost :

= 0.00434763 + 0.0000000326(25)

= 0.004