Question

An employer needs 20,000 units of work (in capacity units) to be performed and can hire as many labourers as needed. Assume that labourers’ only source of income is from this employment and that all income is spent on nutrition. For all payments up to $200 capacity is zero, and then begins to rise by 1.5 units for each additional dollar paid. This happens until an income of $800 is paid. After this point each additional dollar paid increases capacity by one unit. The employer wants to get the work done at minimum cost. How many labourers does the employer need to hire to get the work done? How much would each labourer earn?

Answer 1

On getting paid 800 dollars, a labourer performs 900 units of work. i.e (800-200)*1.5=90

So average work per dollar is 9/8, which is greater than 1, so the employer will hire as much labourer as he can who can work their full capacity upto 900.

So ,20,000/900=22 labourers performing 19800 of work(22*900).The rest 200 of work would be divided among these labourers, because hiring one more labourer would be more expensive ,and these labourers, now that their 800 dollars of income is reached, will work at 1 unit/dollar.

So 22 labourers need to be hired.

So,22*9= 198, the rest two units of work can be done by any two particular labourers.So 20 workers would earn 809 dollars and 2 would earn 810 dollars.Approxing it, each labourer is earning 810 dollars. Total expenditure= 17800

If we consider approximation to 810 dollar per worker., total expenditure= 17820.

(If not understood please ask the doubt in the comments section).