Question
In: Economics
A firm can choose between two production technologies for a new product line. If it installs...
A firm can choose between two production technologies for a new product line. If it installs technology 1, its yearly costs will be: ?1=4500+25?+45?2. If it installs technology 2, its yearly costs will be: ?2=400+125?+?2. What is the marginal and average cost of each technology? What is the minimum efficient scale of both technologies? Which technology would the firm prefer (purely from a cost standpoint) if it expects to sell 60 units each year?
Solutions
Expert Solution
Yearly cost for technology 1 -
C = 4500 + 25q + 45q2
Marginal cost = dC/dq = 25 + 90q
Average cost = C/q = (4500/q) + 25 + 45q
Minimum efficient scale is when AC = MC
q(25 + 90q) = 4500 + 25q + 45q2
25q + 90q2 = 4500 + 25q + 45q2
45q2 = 4500
q = 10
Hence minimum efficient scale is 10.
Yearly cost for technology 2 -
C = 400 + 125q +q2
Marginal cost = dC/dq = 125 + 2q
Average cost = C/q = (400/q) + 125 + q
Minimum efficient scale is when AC = MC
q(125 + 2q) = 400 + 125q + q2
125q + 2q2 = 400 + 125q + q2
q2 = 400
q = 20
Hence minimum efficient scale is 20.
If the company expects to sell 60 units each year
Cost of technology 1 - C = 4500 + 25q + 45q2 = 4500 + 25(60) + 45(60)2 = 168,000
Cost of technology 2 - C = 400 + 125q +q2 = 400 + 125(60) + (60)2 = 11,500
Hence, for producing the same quantity in a year, technology 2 costs much lesser to the company than technology 1. Hence the firm would clearly prefer technology 2 for production.
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