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 enough 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 coffe 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 and in the short run production function? If capital/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 minimizing his Average costs, how may weired looking tables should he produce? What is Ahmad's average cos function? If Ahmad wants to minimize his Average costs, how may 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

Yes, Ahmad can build as using this function he can judge how many labour and capital is required. And he can work on the amount of quantity to be produced also. We see that 0.5+0.5=1; it means constant return to scale. He even knows that doubling the capital and labor will double the output as well.

Output elasticity is 0.5--- he can judge very well the way he can increase i.e. double its productivity; yes he can mechanize its production.

Now k=100; hence Q=2*(100)^(0.5)L^0.5= 20L^(0.5) is the short run production function.

TC=VC+FC

VC=W.L;FC=R.K

W=WAGE AND R= RENT

W=$100 AND R=$200

VC=100L

FC=200K

If k=100;

Then, q=20L^(0.5)

             L=(q/20)^2=q^2/400

TC= 100*(q^2)/400+200*100

TC=0.25*q(^2)+20000

VC=0.25*(q^2)

FC=20000

Average total cost= 0.25(q^2)/q+20000/q=0.25q+20000/q; differentiatewith q to find the minimum average cost.

Equate with q=50 units in the equation and solve as done in case of short run.

TC=0.25*(50*25)+20000 in long run cost will b this.

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