Micro L14 the firm’s supply- production PDF

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Professor Martin Sefton
the firm’s supply- production...

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Lecture 14- the firm’s supply: production Production function- summarises the various ways that a firm can efficiently transform inputs into outputs Assuming labour (L) and capital (K) are the only inputs, the production function is q=f(L,K) It shows only the MAXIMUM amount of output that can be produced from given levels of labour and capital (only includes efficient production processes) In the LR a firms inputs can be adjusted more easily - SR: a period of time so brief that at least one factor of production cannot be varied - LR: a period of time long enough that all inputs can be varied The definition of SR & LR depends on the industry in question - e.g. cleaning services vs. automobile manufacturer Assumptions: Labour is a variable input in SR Capital only variable input in LR Short run production Capital is fixed Labour is variable The SR production function is given by: q SR =f ( L, K´ ) Output q SR is also called the total product of labour - this is the amount of output (total product) that a given amount of labour can produce holding the quantity of other inputs fixed marginal product of labour- the additional output produced by an additional unit of labour, holding all other factors constant. MP L =

∂ q ∂ f ( L , K) = ∂L ∂L

Average product of labour- the ratio of output to the amount of labour employed AP L =

-

q L

Graphical interpretation of a firm’s short-run production function Panel A: Total product of labour rises until the firm employs 20 workers, then falls. Panel B: Average product of labour first rises and then falls. o Usually a firm first gains from better utilisation of capital and from specialisation.

o As employment increases, too many workers relative to equipment (capital), inefficiencies arise. APL curve slopes upward where MPL curve is above it and downward where the MPL curve is below it- why? APL is an average, so adding a larger number increases it and adding a smaller number decreases it. Example: The first three units of labour increase total product by 5 units each; the next unit of labour yields 9 units so APL increases from (5+5+5)/3 = 5 to (5+5+5+9)/4 = 6. This implies that the APL curve’s peak is where the MPL curve crosses it (MAX of APL):

(

)

d APL d ( q /L ) ( dq /dL ) L−q dq q 1 − = =0 = = dL dL L L dL L2 ⇔ ⇔ 1 ❑( MP L − APl ) =0❑ MP L= APl L

The APL for L workers equals the slope of a straight line from the origin to the point on the total product of labour curve for L workers - APL = q/L The MPL, dq/dL, equals the slope of the total product of labour curve. The two slopes are equal when APL = MPL (i.e., at the maximum of the APL curve). Law of diminishing marginal returns Law of diminishing marginal returns- if a firm keeps increasing an input, holding all other inputs and technology constant, the corresponding increases in output will eventually become smaller. - Occurs at L=10 in figure 1 This means that eventually

∂ MP L...