Answer to Question #150120 in Microeconomics for Nwajei Simon

Question

You are the manager of a large but privately held online retailer that currently uses 17 unskilled workers and 6 semi skilled workers at its ware house to box and ship the product sit sells online. Your company pays its unskilled workers the minimum wage but pays these mi skilled workers $12.75 per hour. Thanks to government legislation, the minimum wage in your state will increase from $10.25 per hour to$10.75 per hour on July 24,2017. Discuss the implications of this legislation for your company’s operations and in particular the implications for your optimal mix of inputs and long-run investment decisions.

Answer 1

As a generalized economic fact, skilled or semiskilled workers are more efficient and productive than unskilled ones. Hence if there is a sufficiently large wage differential between them, the firm will replace more semiskilled workers for unskilled workers. But this will be true, assuming that the nature of labor is perfectly substitutable.

Given the condition that the minimum wage has risen from $10.25 per hour to $10.75 per hour, the cost structure of the company changes.

Prior to the new legislation, the firm was paying a total of $174.25 per hour to its unskilled labor force and $76.5 per hour to its semiskilled labor force. After the new legislation, the firm will now have to pay $182.75 for every hour to its unskilled labor force.

Note that the total labor cost before the minimum wage legislation was $250.75 per hour. To make sure that the firm is still operating at the same total cost, it will lay off a certain number of unskilled workers who have become expensive to hire. And simultaneously it will add comparatively less expensive semiskilled workers.

Assume that the firm lays off x unskilled workers and hires y semiskilled workers. Its objective is to keep the total cost unchanged at $250.75:

$(17-x) \times 10.75 + (6+y) \times 12.75 = 250.75 \\ 182.75 -10.75x + 76.5 + 12.75y = 250.75 \\ 8.5 = 10.75x -12.75y \\ 10.75x = 8.5 + 12.75y$

The last equation suggests that the firm can lay off 2 unskilled workers and hires 1 semiskilled worker to maintain the optimum input mix for a total labor cost that stays constant at 250.75:

$10.75x = 8.5 + 12.75(1) \\ 10.75x = 21.25 \\ x ≈ 2$

Hence the legislation changes the optimal input mix from 17 unskilled and 6 semiskilled workers to 15 unskilled and 7 semiskilled workers.