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basic production function
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Q = F (K,L)
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marginal product of labor (MPL)
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change in Q (quantity) / change in L (labor)
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Average Product
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Q (quantity) / L (labor)
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When MP > AP
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AP (average product) is increasing
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When MP < AP
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AP (average product) is decreasing
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When MP = AP
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AP (average product) is at its maximum
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MPl/MPk =
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change in K / change in L
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F (cK, cL) > cf (K, L)
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increasing returns to scale
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F (cK, cL) < cf (K, L)
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decreasing returns to scale
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F (cK, cL) = cf (K, L)
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constant returns to scale
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When TP (total product) = Q (quantity) then Q =
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F (K,L)
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APl =
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Q / L
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MPl =
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dQ/dL
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MPk =
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dQ/dK
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MPl =
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Q / K
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MRTS =
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| change in K / change in L | = dK/dL = - MPl / MPk
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TC (Total Cost)
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FC (fixed cost) + VC (variable cost)
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TC (Q) (in terms of production function)
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K Pk + L Pl
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AFC =
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FC/Q
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AVC =
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VC / Q
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ATC =
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AFC + AVC
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MC
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change in TC (total cost) / change in Q (quantity)
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(when K is constant) MC =
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change in VC (variable cost) / change in Q (quantity) OR w / MP
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(when K is constant) change in VC (variable cost) =
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change in W
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(when K is constant) AVC =
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VC / Q or W/Q
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slope of the isoquant
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- (MPl / MPk) = w/r
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LMC =
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change in LTC / changing in Q or LTC / Q
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Iscocost Curve
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C = wL + PkK
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Slope of isocost =
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- w / r
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Optimal L and K combination
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MPl / MPk = w / Pk
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TVC =
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AVC * Q
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ATC =
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AVC / Q
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TC =
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TVC + TFC or ATC * Q
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TVC =
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w * L
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Log run equilibrium under perfect competition =
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P = SMC = LMC = ATC = LAC
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Elasticity of supply =
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p/q 1/slope or change in p / change in q (P/Q)
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When holding one input fixed: MC =
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dC / dQ
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When AC > OC =
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elastic
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When AC < OC -
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inelastic
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(when demand is perfectly elastic)
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TR = PQ
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A firm should shut down if...
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P < MC
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