A firm chooses between two production technologies for a new product line. Techn

Question

A firm chooses between two production technologies for a new product line. Technology 1 has total costs of production: C1 (q) = 45 + 20q + 2q^2. Technology 2 has total costs of production: C2 (q) = 20 + 20q + 3q^2.

a)What technology is more efficient from a cost standpoint if the expected output is very low, say, 1 unit? Explain intuition behind your answer without explicit calculations of costs.

b) What technology is more efficient from a cost standpoint if the expected output is very high, say 1000 units? Explain intuition behind your answer without explicit calculations of costs.

c) What is the firms long run average cost curve?

Explanation / Answer

Technology 1 has a cost of $4/item and Technology 2 has a cost of $6/item, this is true for infinite number of products. The problem is a derivitive problem where you can figure out the instantanious cost of 1 item by finding the limit of the function as the cost approaches zero. The equation of this (tangent, slope, etc) is lim h->0 f(a+h) - f(a)/h this is just to figure out the instantanious rate of change with reapect to the number of items produced. If you plug in [45 + 20(a+h) + 2(a+h)^2] -[45 + 20(a) + 2(a)^2]/h the slope is 20-4a, likewise for the second equation you get 20-6a. Therefore no matter what amounts are put in, the change is the same. So the cost curve is a constant at C1 = 4 and C2 = 6 after 1 item is produced of course, which would be 24 and 26 respectively.

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