Output Optimization (Production, Cost and Revenue) BEC Managerial Economics

Determining the optimal use of the variable input Assuming that the capital input, or indeed any input in general terms, is fixed, – a firm can determine the optimal amount of the variable input. This involves an explanation of the concepts of marginal revenue product (MRP) and marginal factor cost (MFC). 2

Marginal Revenue Product (MRP) 3

Marginal Factor Cost (MFC) 4

An example: 5

Contd… 6

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Increasing and Diminishing Returns Increasing Returns Decreasing Returns Negative Returns TP Q L AP,M P L AP MP TP L3L2L1 L2 L3 Stage 1 Ep>1 Stage 2 0<Ep<1 Stage 3 Ep<0 Stage 1: average product rising. Stage 2: average product declining (but marginal product positive). Stage 3: marginal product is negative, or total product is declining. Pt of Marginal Returns Ep=0 Ep=1

Returns to Scale An increase in scale involves a proportionate increase in all the inputs of the firm. The resulting proportionate increase in output determines the physical returns to scale for the firm. 10

Extreme Cases of Input Substitutability 11

Types of Returns to Scale Constant returns to scale (CRTS) – This refers to the situation where an increase in inputs results in an exactly proportional increase in output. Increasing returns to scale (IRTS) – This refers to the situation where an increase in inputs results in a more-than-proportional increase in output. Decreasing returns to scale (DRTS) – This refers to the situation where an increase in inputs results in a less-than-proportional increase in output. 12

Economies of Scale Economies of scale (EOS) can be defined as aspects of increasing scale that lead to falling long-run unit costs. – Internal economies arise from the growth of the firm itself In this sense they are controllable and under the influence of management decision-making. – External economies arise from the growth of the industry, and are independent of the size of the firm. They are therefore further removed from managerial decision-making, though not entirely so; location decisions in particular may depend on these economies 13

Technical Economies – These arise mainly from increased specialization and indivisibilities. Managerial Economies – Large firms find it easier to attract and use more specialized managers, who are more skilled and productive at performing specific managerial functions 14

Marketing Economies – These relate mainly in obtaining bulk discounts and advertising economies. Financial Economies – Large firms can often borrow at a lower interest rate, because they have a better credit rating, representing a lower default premium. 15

Diseconomies of Scale Diseconomies of scale (DOS) are aspects of increasing scale that lead to rising long-run unit costs. Again they can be internal or external, physical or monetary, and can arise at the level of product, plant or firm. Technical, managerial, marketing and financial diseconomies. 16

Economies of Scope Economies of scope occur when changing the mix of operations has cost benefits. Ex: Producing 100,000 units of product X may involve a unit cost of $100 if X is produced by itself; but if 100,000 units of X are produced along with a quantity of product Y, then the unit cost of producing X may fall. There are two (02) main causes of this. – The products may use common processing facilities; for example, different car models being produced at the same plant. – There may be cost complementarity, especially when there are joint products or by-products, for example petrochemicals 17

Short-run and long-run average cost functions in the absence of EOS and DOS 18

Short-run and long-run average cost functions with EOS and DOS 19