Question

Assume the short run variable cost function for Japanese beer is VC = 0.590.67 If the fixed cost (F) is $1800 and the firm produces 400 units, determine the total cost of production (C), the variable cost of production (VC), the marginal cost of production (MC), the average fixed cost of production (AFC), and the average variable cost of production (AVC). What happens to these costs if the firm increases its output to 500?

Answer 1

VC =0.5q0.67

FC = 1800

TC= FC+VC

TC= 1800+ 0.5q0.67

MC = dTC/dq = 0.67(0.5)q-0.33 = 0.335q-0.33

q = 400 units

Total cost , TC = 1800+ 0.5(400)0.67

= 1800+ 0.5(55.38) = $1827.69

Variable cost = (0.5)(400)0.67 = $27.69

Marginal cost = 0.335(400)-0.33 = $0.046

Average fixed cost ,AFC= FC/q = 1800/400= 4.5

Average variable cost ,AVC= VC/q = 27.69/400= 0.069

If firm increases its output to 500.

TC = 1800+ 0.5(500)0.67

= 1800+ 32.16 = 1832.16 (i.e TC increases)

VC = 0.5(500)0.67 = $32.16 (i.e VC increases)

MC = 0.335(500)-0.33 = 0.043 (i.e MC decreases)

AFC= 1800/500= 3.6 (i.e AFC decreases)

AVC= 32.16/500= 0.064 (i.e AVC decreases).