Ahmad is a woodworker, specialized on production of weired looking coffe tables.

Question

Ahmad is a woodworker, specialized on production of weired looking coffe tables. Unfortunately, when he was attending his woodworking school 55 years ago, he did not pay attention in the class "Woodworking-Econ 310: Microeconomics for woodworker", and he deeply regrets this huge mistake until today. However, he remembers enought to figure out that his Cobb-Douglas production function for wierd looking coffe table is Q=2K^0.5 L^0.5. Can Ahmad build any weired looking coffee tables without tools? Can Ahmad Completely mechanize the production of weired looking coffee tables? Ahmad currently has 100 units of capital/tools, and in the short run he can neither acquire more tools, nor sell any existing tools. What is Ahmad's short-run production function? If kapital/tools rents for $100 per unit per day, and Labor can be hired for $200 per unit per day, what are Ahmad's fix costs and variable costs? What is his Total cost function? What is Ahmad's average cost function? If Ahmad wants to minimize his Average costs, how many weired looking tables should he produce? What is the long term (meaning: capital/tool level is flexible) cost minimizing amount of labor and capital to produce 50 weired looking chairs.

Explanation / Answer

(a) If there are no tools, then K = 0 for which Q = 0 based on the production function

(b) If there is complete mechanization, then L = 0, Clearly this isnt possible again as Q = 0

(c) here K = 100, thus Short run production function is Q = 20L^0.5

(d) Here w = 200 and r = 100, then TC = 200L + 100K

But K = 100 in short run, then TC = 200L + 10000

Rearrange the production function such that L = (Q/20)^2

Thus, TC = 200(Q/20)^2 + 10000 = 0.5(Q)^2 + 10000

(e) AC = 0.5Q + 10000Q^(-1)

To minimize AC, we differentiate AC function wrt Q

We get d(AC)/dQ = 0.5 - 10000Q^(-2)

Equating this to 0, we get and solving for Q, we get Q = 141.421

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