A firm uses two factors of production: individuals with tattoos and individuals without tattoos, which have...

A firm uses two factors of production: individuals with tattoos and individuals without tattoos, which have different MPs and assume wage of tattooed is < wage of non-tattooed. The firm can hire as many tattooed individuals and non-tattooed individuals as they want at their respective wages. Also, assume that tattooed individuals and non-tattooed individuals are not perfect substitutes for each other in production.

First, show on a diagram the optimal amount of tattooed individuals and non-tattooed individuals the firm would like to employ to minimize costs given q₀. (Put tattooed individuals labor on horizontal axis).

Then, draw a diagram with a potential mix of two inputs given same q₀ when firm has a strong preference for non-tattooed employees. What will happen to this firm in the long run? Why?

Solutions

Expert Solution

Let the firm hire 2 factors of production:

(a) Tattooed individuals labour (X), and (b) non-tattooed individuals labour (Y)

Also, we know that

The firm can hire as many tattooed individuals as non-tattooed individuals.
Wages of X (w_x) < Wages of Y (w_y)
The two factors of production X and Y are not perfect substitutes for each other.

The firms cost is given by the cost equation as follows

We need to minimize this cost given the outout q₀.

The different combinations of X and Y that the firm hires to produce a quantity can be represented by an Indifference Curve. At the optimal bundle or combination of X and Y, the Indifference Curve is tangent to the Cost Line, i.e., the MRS of the goods equals the absolute value of the slope of the cost line.

This can be shown in the figure below.

Where, the slope of the Cost line is

Rahul Sunny answered 1 year ago

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