The Firm and Optimal Input Use Overheads

A neoclassical firm is an organization that controls the transformation of inputs (resources it controls) into outputs (valued products that it sells), and earns the difference between what it receives in revenue, and what it spends on inputs. Nature of the firm

Profit Profit = Revenue - Cost

Objectives of the firm We assume that firms exist to make money, by choosing the optimal levels of inputs and output so they maximize profits

Technology and the firm The technology for a given production process is the set of all input and output combinations such that the output y can be produced from the given set of inputs x

The Producible Output Set P(x) The producible output set P(x) is the set of all combinations of outputs that are obtainable from a fixed level of inputs

Production Functions The production function is a function that gives the maximum output attainable from a given combination of inputs

Example production function

Production and factor costs in the short run Total (physical) product - TPP Total product (y) is the maximum quantity of output that can be produced from a given combination of inputs It is the value of the production function y = f (x 1, x 2,..., x n )

Marginal (Physical) Product (MPP) Marginal (physical) product is the increase in output that results from a one unit increase in a particular input

Marginal Revenue Product (MRP) The marginal revenue product of an input is the increase in output that results from a one unit increase in that particular input

Marginal Revenue Product (MRP) is given by For a competitive firm, MRP is given by

xyDMPPMRPMFC

Marginal Product & Marginal Revenue Product Input DMPP MRP

Marginal Factor Cost (MFC) The additional amount that the firm has to pay for a factor when it hires one more unit of the factor is called marginal factor cost For a firm that is a price taker in the input market, marginal factor cost is equal to factor price MFC i = w i

The Profit Maximizing Output Level The marginal approach to profit maximization says that the firm should take any action that adds more to revenue than to cost

The Profit Maximizing Rule The firm should use another unit of the ith input as long as the marginal revenue product of the input is larger than the marginal factor cost of the input

Marginal Product & Marginal Factor Cost Input MRP MFC x opt

Demand for a variable input (single input) When the firm only uses one variable input, the downward sloping portion of the marginal revenue product curve is the input demand curve The input demand curve tells us how many units of the input the firm will chose to employ at various prices

wxMRP

MRP MFC Input Demand MFC 1 MFC 2 MFC Input $

Summary of results on the firm Profit Maximization p × MPP i = w i, i = 1, 2, …, n

The End