Question

Problem 6. The Marginal Benefit of hiring workers for a firm is given by the expression: MB 3,500 X. The Marginal Cost to the firm of hiring workers is approximately given by the expression: MC = 5000.01X~. Please calculate the optimal amount of workers that the organization a. should hire. Draw a diagram of the solution b. Briefly explain the slopes of the Marginal Benefit and Marginal Cost Curves. Why does it cost more to hire each additional worker? Why the benefit of each additional worker decreases? C. d. Calculate the net benefit of hiring the 10 worker? e. If the wage of the workers increase what will the firm do? Illustrate the solution.

Answer 1

a)

Workers should be hired till the point where

MB MC 3500 X 500 0.01X2 -1 14* 0.01 3000 0.01X2X 3000 0 -111 (Only positive root considered) X 500 0,02 0,02

Hence optimal amount of workers hired by firm = 500

b)

+ 6000 y= 3500 - x X 500+0.01x v = 5000 3 4000 3000 2000 1000 -1000 2000 3000 0 1000 4000 powered by MB/MC

c)

Slope of MB:

dy -1 <0 MB dr

Marginal benefit from hiring a worker is constant i.e. benefits from hiring a new worker is decreasing at a constant rate.

This decreases because of diminishing marginal returns.

Slope of MC:

dy 0.02.x0 MC dr

Marginal benefit from hiring a worker is positive and increasing with each worker. As each worker increases, marginal benefit provided by it decreases. Hence additional cost is incurred to substitute for that.

d)

10 10 MB 3500 x B (3500 x)dr 3500 3500r _ JO 10 50 34950

Hence net benefit from hiring 10th worker = 34950 units.

Net benefit from hiring 10th worker =