Question

Cost of producing 75 units of a commodity is Rs. 275 and cost of producing 150 units is Rs. 300. Assuming that TC is linear, find the (i) cost function. (ii) average total cost of producing 75, 150, 225 units respectively, (iii) average fixed cost of producing 75, 150, 225 units respectively. (iv) average variable cost of producing 75, 150, 225 units respectively

Answer 1

(i) Let the cost function be TC = ax + b.

We have TC(75) = 275 and TC(150) = 300

75a + b = 275 (1)

150a + b = 300 (2)

(2) - (1) $\implies$ 75a = 25 ⟹ a = ${1 \over 3}$

(1) $\implies$ 75(${1 \over 3}$ ) + b = 275

b = 275 - 25 = 250

TC = ${1 \over 3}$ x +250

(ii) average total cost of producing 75, 150, 225 units respectively:

ATC (75) =( ${1 \over 3}$ 75 + 250) / 75 = 3.67

ATC (150) =( ${1 \over 3}$ 150 + 250) / 150 = 2.00

ATC (225) = (${1 \over 3}$ 225 + 250) / 225 = 1/44

(iii) average fixed cost of producing 75, 150, 225 units respectively:

AFC (75) = 250 / 75 = 3.33

AFC (150) = 250 / 150 = 1.67

AFC (225) = 250 / 225 = 1.11

(iv) average variable cost of producing 75, 150, 225 units respectively:

AVC (75) = ${1 \over 3}$

AVC (150) = ${1 \over 3}$

AVC (225) = ${1 \over 3}$