Question

2. With the help of calculus, prove the following. w MP a. The condition for cost minimizing combination of labor and capital isMP MP c. The condition for profit maximization is MC MR

Answer 1

Cost minimization is a basic rule used by producers to determine what mix of labour and capital produces output at lowest cost .in other words what the most cost effective method of delivering goods and services would be while maintaining a desired level of quality

An essential financial strategy it is important to understand why cost minimization is important and how it works

                                           short run: q= f(L)

                                          long run: q=(K,L)

in the long run a producers has the flexibility over all aspects of production how many workers to hire how big of a factory to have what technology to use and so on. in more specific economic terms a producers can vary both amount of capital and the amount of labour it uses in the long run

therefore the long run production function has 2 inputs capital (K) and labour (L).in the table provided here q represents the quantity of output that is created

choices of production function:

                                           short run : q=f(L)

                                           long run : q=f(K,L)

in many business there are a number of ways in which a particular quantity of output can get created .if your business is making sweaters for example you could sweaters either by hiring people and buying knitting needles or by buying or renting some automated knitting machinery

in economic terms ,the first process uses a small quantity of labour (I.e labour sensitive) wheras the second process uses a large quantity of capital and a quantity of labor (i.e is capital intensive).you could even choose a process that is in between these 2 extremes.

given that there are often a number of different ways to produce a given quantity of output ,how can a company deside what mix of capital and labour to use not surprisingly companies ARE GENERALLY going to want to choose combination that produces a given quantity of output at the lowest cost

one opetion would be to map out all of the combinations of labour and capital that would yield the desired quantity of iutput calculate the cost of each of these options and then choose the option with the lowest cost unfortunately this can get pretty tedious and is in some cases not feasible

luckily there is a simple condition that companies can uses to determine whether can used to determine wheather their mix of capital and labour is cost" MINIMIZING"

2.MC stands for marginal (extra) cost incurred by a firm when its production raises by one unit .MR stands for marginal (extra)revenue a firm receives from producing one extra unit of output . as a firm is trying to maximise its profits ,it needs to consider what happens when it changes its production by one unit .the firm will of course incure an extra cost from producing an extra cost from producving an extra unit. if the marginal cost is bigger than the marginal cost is bigger than the fiurm should realise that producing an extra unit of output was not profitable .the firm should thus cut down some of its production .if the marginal cost is smaller than the marginal revenue then it is profitable for the firm to produces an extra unit of output. the firm to produce extra units of output as long as the marginal revenue it receives from that unit exceeds the marginal cost. the firm should continue doing this until exceeds the marginal cost. the firm should continue doing this until MC=MR a point at which they should keep production constant because producing an extra unit beyong this point creates a higher marginal cost for the firm that it creates marginal revenue.