Optimal combination of resources

Optimal combination of resources

How much of each resource should be hired?

Land “A” for acreageLabor “L” Capital “K”We won’t be using entrepreneurs

diminishing Marginal Utility and Utility Maximization Theory. 

   

Remember the concept of diminishing Marginal Utility and Utility Maximization Theory?As we consume more of a product our utility diminishes.  When we purchase goods we purchase goods so as to maximize our Marginal Utility per $$$ 

MUa/Pa = Mub/Pb What do you do if they are not equal???? 

Optimal Combination of Resources: Given all the resources you must choose the combination that produces the most for the dollar.  

Firms can vary the amount of their inputs. In so doing they will try to produce using the combination of resources that maximizes profits and minimizes losses. 

 

The Least-Cost Rule: 

Assume two resources: labor and capital 

The cost of any output is minimized when the marginal product per dollar's worth of each resource used is the same. MP= MPP: change in production from additional resource 

(This is basically the same formula as we used for determining Utility Maximization)

MP of labor = MP of capital price of labor price of capital

MPl = MPk Pl PkWe want the return on each dollar spent to be equal.So what do we do if it’s not?

What if MPl is 50 and MPk is 25 with the price of both being 1?

You would be better hiring more labor because you are getting more for your dollar. What if the MPl/pl = 50/2 and MPk/pk = 50/1

In this example the firm will take a dollar away from labor and give it to capital. This moves capital down its MP curve for capital and up the MP curve for labor.

The net result of this is that we gain 50 units from capital and lose 25 units from labor. The net result is an increase in MP of 25 units/dollar. 

You have now increased output without increasing costs.  

This is the same thing as producing the same amount of a good at a lower cost.

  

The Profit-Maximizing Rule:

NOTICE THAT MRP IS MP X PRICE 

Now that we have figured out how to produce at the least cost we must look at how to maximize our profit in terms of output. In order to maximize profit from a cost standpoint you should hire resources so that the price of the resource (Pl) is equal to the MRP of the resource (MRPl). (MRC = MRP or Pl = MRPl) 

Pl = MRPl take this and divide both sides by the Pl and you get 

MRPl = 1 Pl

 When you look at this the additional cost of hiring the additional worker is

their price. This means that in effect P1 = MRC. This means this is MRP1/MRC1 = 1. Our rule is hire until MRP = MRC.

Now what do you do when you add in other resources? 

MRPl = MRPk = MPR... = 1 Pl Pk P...

 If all of these are equal, and equal to one then you are in the profit

maximization point.  

*** If any one of these is more than the others then you need to use more of that resource. *** 

Notice that a firm could satisfy the least-cost rule but do so in such a manner that it is producing the wrong quantity. In order to fix this it must look at the profit maximization rule.   

    

FIND OUT THE LEAST COSTLY WAY OF PRODUCING 50 UNITS.Start by finding a combination of labor and capital that will give you 50 units of TP.

Then decide if how much it costs you.Does it meet the least cost rule? Try another way

Labor (price =$8)   Captial (price =$12)

Q TP MP MP/P TR MRP   Q TP MP MP/P TR MRP

0 0 0   0 0   0 0 0   0 0

1 12 12 1.5 24 24   1 13 13 1.08 26 26

2 22 10 1.25 44 20   2 22 9 .75 44 18

3 28 6 .75 56 12   3 28 6 .5 56 12

4 33 5 .625 66 10   4 32 4 .33 64 8

5 37 4 .5 74 8   5 35 3 .25 70 6

6 40 3 .375 80 6   6 37 2 .166 74 4

7 42 2 .25 84 4   7 38 1 .083 76 2

Practice activity in class: Optimal use of resources