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=2K0.5 L0.5. 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

Q = 2K0.5L0.5

(a) Output is a function of capital (tools), so Ahmad cannot build anything without using tools.

(b) Output is a joing funciton of capital as well as labor, so complete mechanization is not possible.

(c) K = 100

Short run production function: Q = 2 x (100)0.5 x L0.5 = 2 x 10 x L0.5 = 20 x L0.5

(d) In the short run, capital (tools) is fixed. So, cost of tools is fixed cost (FC).

FC = $100 x 100 = $10,000

Cost of labor is variable cost (VC).

VC = $200 x L

Total cost: TC = FC + VC = $10,000 + $200 x L

Since Q = 20 x L0.5,

L0.5 = Q / 20

Squaring both sides,

L = Q2 / 20

TC ($) = 10,000 + 200 x (Q2 / 20) = 10,000 + 10 x Q2

(e) Average cost, AC = TC / Q

AC = (10,000 / Q) + 10Q

AC is minimum when dAC / dQ = 0

- 10,000 / Q2 + 10 = 0

10,000 / Q2 = 10

Q2 = 1,000

Q = 31.62 units

Note: First 5 sub-questions are answered.

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