# Behind The Supply Curve: Production Function I

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Behind The Supply Curve: Production Function I
1. Production - short run Productive efficiency The Law of diminishing marginal returns 2. Production - long run isoquants & isocosts least cost method of production

Background Firms seek to maximise profit ()
 = R - C How do firms produce output and minimise costs (C)? What is production? “…production is simply the process of transforming inputs and outputs.” inputs = capital (K) and labour (L)

A production function Functional relationship Productive efficiency
Q = f(K, L , T) T changes over time At a point in time T is fixed Productive efficiency “A method of production is efficient if, for a given level of factor inputs, it is impossible to obtain a higher level of output, given the existing state of technology.”

The short run Period of time over which one factor is fixed
Capital - machines, factory, etc. Total and Marginal Physical Product “…marginal product is the additional output produced by an additional unit of labour MPP = TPP / L See Figure

Wheat production per year from a particular farm
TPP Tonnes of wheat produced per year fig Number of farm workers

Wheat production per year from a particular farm
TPP Tonnes of wheat per year Number of farm workers (L) Tonnes of wheat per year Number of farm workers (L) fig MPP

Law of Diminishing Returns
Definition “…as units of one input are added (with all other inputs held constant), a point will be reached where the resulting additions to output will begin to decrease; that is marginal product will decline.” On figure - between 2 and 3 workers

2. The Long Run All factors are variable Decisions Choice of technique
Scale Location Technique Choice of technique Isoquants Isocosts

Isoquants An isoquant Construction, slope and maps
“…is a contour line which joins together the different combinations of two factors of production that are just physically able to produce a given quantity of a good.” Construction, slope and maps

An isoquant Units of K 40 20 10 6 4 Units of L 5 12 20 30 50
Units of capital (K) fig Units of labour (L)

Diminishing marginal rate of factor substitution
MRS = 2 MRS = DK / DL DK = 2 h DL = 1 Units of capital (K) isoquant fig Units of labour (L)

An isoquant map Units of capital (K) I5 I4 I3 I2 I1
fig Units of labour (L)

Isocosts Actual output also depends on costs isocosts
join combinations of K & L - same cost assuming constant factor prices Construction, slope & map

An isocost Assumptions PK = £20 000 W = £10 000 TC = £300 000
Units of capital (K) TC = £ fig Units of labour (L)

Finding the least-cost method of production
Assumptions PK = £20 000 W = £10 000 TC = £ Units of capital (K) TC = £ TC = £ TC = £ fig Units of labour (L)

Finding the least-cost method of production
Units of capital (K) TPP1 fig Units of labour (L)

Least cost method of production
Tangency between isoquant and isocost Where: Slope of isoquant = slope of isocost Successive points of tangency - scale expansion path

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