Determining the level of labour and capital that maximises profits:
Capital and labour are used in the production process and they are referred to as factors of production, however the unit cost of capital and labour sometimes differs and therefore firms have to make decisions on what quantities of capital and labour are required in order to reduce the cost of production which in turn will lead to increasing the profit levels.
The cost of labour and capital are the most important things to consider when one to determine the quantities of both, when the cost of capital is higher than the cost of labour then we substitute capital for labour and if the cost of labour is higher than the cost of capital then we substitute capital with labour.
If we consider the production function where Q is the level of output, then Q = F (K, L) output is a function of both capital and labour, however to determine the optimum level of output that will maximize profit we will have to consider the cost of one unit of labour and one unit of capital and further consider the budgeted amount.
Given that the cost of one unit of labour is 5 pounds and that the cost of one unit of capital is ten
pounds and that our budget for both costs is 100 pounds then our optimum point will be determined as follows.
The maximum amount of capital that can be purchased is 100/10 = 10 and the maximum amount of labour that can be purchased is 100/5 = 20, this information will help us determine the budget line. The next thing to consider is the isoquant, isoquant are curves that depict the possible output that is derived from two factors of productions which in this case are capital and labour
The diagram below shows the optimum level of production:
The isoquant depicts the level of output that can be produced by different combinations of capital and labour, we determine the most optimum combination of capital and labour by determining the point where the budget line touches the isoquant, and therefore our most optimum levels of capital is C’ and for labour its L’ as shown above. Therefore the information that we need to collect is the unit cost of both capital and labour and the budgeted amount so as to determine the budget line and also we need information that will help us determine the isoquant.
When determining on what to produce either cooking pans or sinks we need to determine the cost of producing in terms of capital and labour for each item and also the market price of each item, given that the level of capital and labour are fixed in this case then we have to determine the optimum level of output for both products. This analysis will take the form of the consumer utility maximizing function where there exist two products, the utility function will represent the revenue collected by the firm and the two products which the consumer chooses will represent the two products produced by the firm.
If in total we have 200 units of resources (both capital and labour) and that one sink requires 10 units of resources and one cooking pan requires 5 units of resources, then the maximum units of sink that can be produced is 200/10 = 20 and for the cooking pans is 200/ 5 = 40,
Resource Production line
The revenue curve will be determined by the market price of both products, it combines the possible amount of revenue that can be obtained by different combinations of cooking pans and sinks, the additional information needed therefore is the market price for both products and the amount of resources needed to produce each product.
In the long run the firm will tend to expand its production capacity in order to produce the optimum amount of both products, when the firm increases its capacity more products will be produced in order to realise economies of scale, however the average cost of production for the firm will decrease in the short run but will increase in the long run
The long run and short run average cost curve
Short run average cost curves
Long run average cost curve
The average cost curve will decrease in the short run when the firm expands its capacity but will increase in the long run as shown in the diagram above.
If the products exhibit constant returns to scale then we would tend to produce more for both products but we will produce more for the product requires less amounts of labour and capital and therefore the firm will realise more profits
Anthony Samuelson (1964) Economics, McGraw-Hill publishers, USA
W. Shepherd (1983) Cost and Production Functions, Princeton University Press, Princeton
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