Given the above data what we have to determine is whether or not the rule for the optimal combination of factors of production holds given these two factors of production. The rule for the optimal combination of factors of production states that the firm is using its factors at an optimal level where:
MPC/Pc=MPL/PL
In other words the marginal product per pound of labour (MPL/PL) and capital (MPC/PC) must be equal. If this condition doesn’t hold then the firm isn’t being economically efficient. This is because what this condition represents is the point of tangency between the isoquant and isocost curves and it is at this point that the firm operates at the highest possible isoquant curve given its cost constraint as illustrated in the following diagram. This is because at this point the slope of the isocost curve (PL/PC) is equal to the slope of the isoquant curve (MPL/MPC) and we obtain the above formula simply by setting these two slopes equal and re-arranging. In the following diagram we see IC1, IC2 and IC3 which represent different input mixes that yield the same output, so we see that if we change isoquant our output will change. We also see the isocost curve ISC which represents the different input mixes we could obtain, given our budget.
As seen in the above figure the budget constraint limits us to all the points below it. Thus the firm could produce on any point A, B or C and be technically efficient, in other words use the minimum amount of factors of production. However, there is only one combination that is economically efficient, in other words that the firm can use the minimum amount of factors of production to yield the desired output at the minimum cost and this is at point B. This is because at point B the firm operates on the highest isoquant possible and this is why determining the point at which the slope of the budget constraint is equal to that of the isoquant gives us the point of economic efficiency for Mauritours.
1/3 must equal 1/4
What the firm must do is increase its use of capital so that its marginal productivity will decline and thus the ratio on the left hand side of the formula will decrease and decrease its use of labour so that its marginal productivity will increase and thus the right hand side of the formula will increase. The firm will have to continue doing this until it has reached the point where these two ratios converge. The reason why it will change its use of labour and capital so as to affect their marginal productivity is because the firm has no control over their price so in order to increase or decrease the ratio it can only change the number of factors it employs so as to affect their marginal productivity. It is very important to note down that there must be a trade off between the two so that output remains constant, if we alter the one factor but not the other then we will operate on a different isoquant which as a result won’t be tangent to our budget constraint and thus won’t represent a point of economi c efficiency. Overall the reason the firm chooses to operate at the point where the slope of the isoquant curve equals the slope of the isocost curve is because at that point it generates the maximum output for its input.
This can be illustrated arithmetically by assuming that we increase the use of capital by one unit and reduce our labour consumption by 2 units we see that our output remains the same however our cost has been reduced by £10 proving that the firm wasn’t at the point of optimum economic efficiency before.