**Tightening law enforcement against illegal workers in the US can increase real wages. (True/False)**

This is one of the questions from the 'Macroecomoics Problem Set' for the MIT students. Actually, first I thought this statement is false. My reasoning was assuming all the other factors are constant (tax rates, people consumptions, production rate, etc) the wages could increase in one place but decrease at the other. So, there will not be any change and thus it will remain constant. So, the answer would be 'False'.

I tried analyzing it with an example. But the output I got was totally reverse from what I have thought. The Output was showing an increase. (The correct answer is there would be an increase)

Here is my logic:

Let us assume a tax free country (so I do not want to do some extra tax calculations) in the following proportion.

Total Members in the country = 100

**Split Up**

Number of legal workers = 15

Number of illegal workers = 05

Number of owners = 10

Number of consumers = 20

**Salary Details**

Salary for 1 legal worker/month = 10

Salary for 1 illegal worker/month = 05

Let us assume each owner gets a amount (after work related & miscallaneous expenses) of 100 dollars.

**Wage Details -A**

Total amount with the Owners = 100 * 10 = 1000

Salary for Legal Workers = 15 * 10 = 150

Salary for Illegal Workers = 05 * 05 = 25

Total Profit = 825

30% of the total profit is reinvested in the business.

Remaining amount = 577.5

This remaining amount is the actual wage for the 10 Owners.

So, Total amount of wages

= Wages for (Legal Workers + Illegal Workers + owners)

= 150 + 25 + 577.5

=

**752.5**

Now, Let us assume the following:

1. 5 illegal workers are removed. This leaves with only 15 legal workers.

2. The number of consumers remain constant

3. Due to scarcity of workers, the legal workers salary is increased by say 5%.

4. The work remains the same.

**Calculation of Increased Salary**

Number of working hours 20 workers * 40 hours * 4 weeks

= 3200 hours

Number of working hours for legal workers = 2400

Total salary for legal workers = 150

So, per hour salary for legal workers = 0.0625

5% of 0.0625 = 0.003125

Total Salary = 0.065625

Total Salary for 3200 hours (point (4) above) = 210

**Wages Recalculation - B**

Total amount with the Owners = 100 * 10 = 1000

Salary for Legal Workers = 210 (Refer the calc above)

Total Profit = 790

30% of the total profit is reinvested in the business.

Remaining amount = 553

This remaining amount is the actual wage for the 10 Owners.

So, Total amount of wages = Wages for (Legal Workers + owners)

= 210 + 553

= 763

So this shows

**an increase in 10.5$**.

On analysis of the above scenario, it is clear where this difference is occuring.The 30% total profit reinvested in the business. If that reinvested amount would be considered as wages for the corporation (remember, corporation are completely independent from the owners) then the total wages would be:

**A**

So, Total amount of wages

= Wages for (Legal Workers + Illegal Workers + owners + Corporations)

= 150 + 25 + 577.5 + 247.5

= 1000$

**B**

So, Total amount of wages

= Wages for (Legal Workers + Illegal Workers + owners + Corporations)

= 210 + 553 + 237

= 1000$

Thus my initial argument will hold good. But, Is it valid to call the reinvestment amounts as "wages for the corporation".Also, I do not know whether the process that I have followed is valid/correct... If someone could say whether it is correct/ wrong, it will greatly helpful.....

**P.S**

The University's answer is provided below:

True: The labor supply curve will shift up-left and a new equilibrium with a higher real wage will exist. This is, in part, due to the pro-cyclical mark-up assumption.

## 4 comments:

If you don't consider business owners profits as wages then the numbers are 175 for case A and 210 for case B. I think that is the usual case.

Another way to see it is not use 30% reinvestment but assuming a fixed amount is required for reinvestment (assuming you didn't do anything wasteful in reinvesting) say 247.5 (30% of 825). Then case A remains same. Case B "Remaining Amount" will be 790 - 247.5 = 542.5 .

So total wage will be 752.5. There are no changes in wages if you look at it this way. But we know the wages of workers increased.

I think you should leave the profits of owners out.

But that was my central theme right. The owners and the business (corporations) are 2 different entities and thus the money goes to the owner is considered as the wages provided by the corporation.

I think I could leave the corporation part so the statement would become true.

As we discussed the profits* of the owner will increase/decrease when the wages of the rest(legal+illegal or just legal) decrease/increase. The total wages then will always be constant (752.5 here) as 247.5 of reinvestment is a constant.

If you consider the owner himself as a legal worker then I think he must have a fixed wage. If you just consider his wage as all the profits then his wage will vary like *. So the wages will remain constant for legal workers+owner in that case as one will adjust the other. But I don't think we should consider the owner's profits.

If you want give a fixed wage to the owner. Even then the wages will rise as the owner's wage will remain constant and the wages of the rest will increase.

Yes. Now I get the point. Now I am able to understand it...

Economics is also seems to be interesting... :-)

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