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ECO206 notes - lec 7

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University of Toronto St. George
Gordon Cleveland

Principles of Economics: Short-run Cost We first examine the cost of firms in the period when capital is fixed to understand the importance of marginal cost in the determination of profit maximizing output. We do this by deriving cost functions from production functions. SHORT-RUN PRODUCTION AND COST FUNCTIONS Production Function Definition: The set of all maximum possible outputs from a given input or inputs that provide a technologically feasible way to produce a commodity or service. Q = f(Xo, X 1 X 2 X 3 X4, X N where Xi represents the inputs into production We simplify this by dividing the inputs into Capital (K) and Labour (L) to get Q = f(L, K) Firm Definition: A business organization producing goods and services from resource inputs Business implies the assumption of profit maximization The firm connects costs and output as the smallest unit of production. Industry Definition: All the firms that produce a given good or service Short-run Definition: The period in which one factor (input) is fixed Long-run Definition: The period in which all factors are variable Variable Inputs Definition: Inputs that vary in quantity with each additional unit of output - 1 - Principles of Economics: Short-run Cost Variable inputs include Labour, Fuel, and Raw Materials but we use Labour (L) to represent them all Fixed Inputs Definition: Inputs that do not vary in quantity with an additional unit of output Fixed inputs include equipment and machinery, buildings, and land but we use Capital (K) to represent them all SHORT-RUN PRODUCTION FUNCTIONS Total Product of Labour (TP ) L Definition: The total output produced from each total labour output given fixed capital TP = L = f(LK) (Q = output of the industry and q = output of a firm so that Q = nq where n = #firms in the industry) Average Product of Labour (AP or siLply AP since we will assume that capital is fixed) Definition: Average output of each labour unit given fixed capital AP = L/L Marginal Product of Labour (MP or siLply MP) Definition: The change in output due to a change in labour given fixed capital MP = qLL [(q q )/(1 0 ) f1r di0crete changes] (or = dq/dL for infinitesimal changes in Labour) NOTE: The Marginal Product of Labour is often expressed as the change in output due to an additional unit of labour. - 2 - Principles of Economics: Short-run Cost Law of Eventually Diminishing Returns Definition: Marginal Product eventually decreases with increases in labour since the efficiency of additional labour eventually falls due to fixed capital e.g. The following table shows the Total Product, Average Product, and Marginal Products for units (days) of labour at cotton cloth manufacturer with a spinning, weaving, and dyeing machine. The equation q = - L + 12L describes the total product of labour. Labour Units Total Product Average Product Marginal Product Marginal Product (TP) (AP) MP = L n+1 Ln MP = dTP/dL 1 11 11 11 21 2 40 20 29 36 3 81 27 41 45 4 128 32 47 48 5 175 35 47 45 6 216 36 41 36 7 245 35 29 21 8 256 32 11 0 9 243 27 -13 -27 Marginal Product initially rises because additional workers can use the fixed capital more efficiently but eventually marginal product declines because the fixed capital limits the productivity of the workers. Marginal Product declines to below 0 when an additional worker results in a fall in Total Product, not just a decline in Marginal Product. Notice that Total Product shows us that output increases up to 8 workers and then decreases but does not show us the rate at which Total Product increases or decreases. Marginal Product is more informative since positive (negative) Marginal product tells us not only whether Total Product increases (decreases) but also the change in Total Product. The diagram below shows the output as a function of Labour in the upper diagram and output per worker as a function of Labour in the lower diagram. Total product is a function of total labour - 3 -
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