What is the profit maximizing number of workers to employ in this operation? How

Question

What is the profit maximizing number of workers to employ in this operation?

How much will you pay these workers?

What is the marginal contribution these workers will provide for your firm’s gross revenues?

What is the marginal profit these workers will provide to your firm?

Suppose you're a senior level manager in a manufacturing firm for which moderately skilled labor is required to assemble and test technical products. The labor supply relation (Ls) in your market is parameterized by the equation Ls15+4W. Though you're not the only employer in your market, you're clearly the largest and the only f?rm of any real size offering jobs at a living wage. You produce a composite material in a specialized environment used by many high tech manufacturers in a highly competitive, national goods market, and you sell this component for $2 per unit, and the material can be manufactured and sold in fractional units. Your accounting group has recently completed an audit of your operation and that of similar operations in other markets. Though these are accountants and may not really understand the basis of the labor economic metrics with which you manage your operation, they're noted that your firm's labor demand relation should be LD 100-W. You understand that this may not be all that meaningful, but you do want to them to provide you with a table indicating what quantity of output they've observed at varying wage levels. They provide you with the following data and you go about your job to identify the optimal number of workers for your firm to maintain profit maximization with respect to labor. Hint: if you come up values such that it might seem you're very close to one solution, but not exactly there... check your math and scrutinize how you've rounded. It could make a big difference in how you answer the following questions!

Explanation / Answer

Consider the given problem here the demand and the supply of labor is given by.

=> “Ld = 100 – W” and “Ls = (-15) + 4W” respectively, => at the optimum the “Ld” must be equal to “Ls”.

=> Ld = Ls, => 100 – W = (-15) + 4W, => 5W = 115, => W = 115/5 = 23, => W =23.

So, the labor hiring is given by, => Ld = 100 – W = 77, => Ld = Ls = 77.     

So, here the profit maximizing numbers of workers to employ is given by, “Ld=Ls=77” and the wage is “W=23”.

b).

So, as we know that the profit maximizing condition is given by, “W = MRPL = P*MPL”.

=> MPL = W/2 = 23/2 = 11.5. So, here the “MRPL = W = 23”, => the marginal contribution on gross revenue is “MRPL = 23”.

c).

Now, as we know that “W=23”, => addition cost to hire additional unit of labor is “23” and under profit maximizing condition “MRPL=W=23”, => additional labor can earn additional revenue “23”, => the marginal profit is “0” and the profit is maximum.

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