Question

Bob Thomason produces theorems using hours of labor and Big Machines. In the short run, his labor is a variable factor but the number of Big Machines is fixed. When he works for L hours using M Big Machines, Bob can produce L-M theorems. There are only 3 Big Machines in the world, and they can only be rented in whole number quantities (you can.not employ 1/2 of a Big. Machine). Bob's time is worth $1 per hour, and it costs $1 per hour to rent a Big Machine. 1. Draw Bob's short run average cost curve on the assumption that he employs 1 Big Machine. Do the same on the assumption that he employs 2 Big Machines. Do the same on the assumption that he employs 3 Big Machines. 2. Draw Bob's long run average cost curve..

Answer 1

1. Production function and the costs of factors of production are:

In the short run, M is fixed at 1. The production function is: $q=L$

Cost associated with this production function is

$Cost=w_LL=q \because w_L=1, L=q$

Average Cost is 1

When M is fixed at 2, the production function is: $q=2L$

Cost associated with this production function is

Cost Wi L =

Average cost is 0.5

When M is fixed at 3, the production function is: $q=3L$

Cost associated with this production function is

Cost Wi L 3 =

Average cost is 0.33

2. In the long run, the production function is: $q=LM$

At equilibrium, the marginal rate of technical substitution is equal to the ratio of the factor prices:

$\frac{M}{L}=1 \rightarrow L=M$

Using this value of L, the production function is: $q=L^2 \rightarrow L=\sqrt{q}$

Cost associated with this production function is:

$Cost=w_LL+w_MM=\sqrt{q}+\sqrt{q}=2\sqrt{q}$

Average cost is

$\frac{2}{\sqrt{q}}$

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