Question

A firm currently uses two inputs, 5 units of skilled labor (Ls) and 40 units of unskilled labor (Lu), to produce its output. Input prices equal $100 per hour for skilled labor and $10 per hour for unskilled labor. The firm's current input combination is cost-minimizing.

1. Put numbers in the blanks to derive the equation for the total cost:

The firm's total cost (TC) = _________* Ls + _______* Lu

b. And use this TC equation to draw an isocost line. Put skilled labor (Ls) on the x-axis. Use numerical values to label the isocost endpoints and the current input combination.

c. Suppose that the wage for skilled workers falls to $50 per hour. If the firm wants to continue to produce the same level of output (i.e. no scale effect), what input adjustment should the firm make?

1. Switch from skilled worker to unskilled worker
2. Switch from unskilled worker to skilled worker
3. The firm does not adjust the input combination
4. More information is needed to determine.

Answer 1

(a)Input price for skilled labor= $100 per hour

Input price for unskilled labor = $10 per hour

TC = 100 Ls + 10 Lu

(b) Currently , Ls = 5 units and Lu= 40

This implies TC= (100)(5)+ (10)(40)= $900

900 = 100Ls + 10 Lu

When Ls =0 , Lu= 90

When Lu=0 , Ls = 9

By plotting these points, we get the isocost line and the current input combination.

(c) Suppose wages for skilled labor falls to $50 per hour.Then ,the firm should switch from unskilled worker to skilled worker.