Fbasic background of firm´s analysis Fshort run production function Ffirm´s production in long run, firm´s equlibrium Ffirm´s equilibrium upon different levels of total costs, and prices of inputs Freturns to scale Fexamples of long run production functions Ffirm = subject producing goods and/or services... transformig inputs into outputs Ffirm: recruits the inputs Ò organizes their transformation into outputs Ò sells its outputs Ffirm´s goal is to maximize its profit Feconomic vs. accountable profit Fekonomic profit = accountable profit minus implicit costs Fproduction limits – technological and financial Fproduction function – relationship between the volume of inputs and volume of outputs Fconventional inputs: labour (L), capital (K) Fother inputs: land (P), technological level (τ) Fproduction function: Q = f(K,L) Fshort run – volume of capital is fixed Flong run – all inputs are variable A A' B' B C C' L L TPL MPL APL MPL APL to A – increasing returns to labour (MPL increasing) to B – 1st stage of production – average product of labour and capital are increasing; motivation to increase production, fixed input not fully utilized between B and C – 2nd stage of production – average product of labour decreasing, but AP of capital still increasing behind C – 3rd stage of production – both APs decreasing, total product decreasing firm endeavours the 2nd stage of production TPL FMPL = product of additional unit of labour Fwe add: a) additional working hours... or b) additional workers? Fa): MPL influenced with human´s nature Fb): MPL influenced with the nature of production FQ = f (Kfix, L) FAPL = Q/L APK = Q/K FMPL = ∂Q/∂L MPK = ∂Q/∂K Q L L APL MPL APL MPL TP Total product increases with increasing rate – TP grows faster than the volume of labour recruited Q L L APL MPL APL = MPL TP TP increases with constant rate – as fast as volume of labour recruited L L APL MPL MPL TP APL Q TP increases with decreasing rate – TP grows slower than the volume of labour recruitet Fboth inputs, labour and capital are variable FQ = f(K,L) FLR production function as a „map“ of isoquants Fisoquant = a curve that represents the set of different combination of inputs leading to the constant volume of total product (output) – analogy to consumer´s IC 0 L K Q1 Q2 Q3 If both inputs are normal, total product grows with both inputs increasing Fanalogy to ICs F... are aligned from the cardinalistic point of view (total product is measureable) F... do not cross each other F... are generally convex to the origin (a firm usually needs both inputs) FMRTS – ratio expressing the firm´s possibility to substitute inputs with each other, total product remaining constant (compare with consumer´s MRSC) FMRTS = -ΔK/ΔL F-ΔK.MPK = ΔL.MPL → -ΔK/ΔL=MPL/MPK → MRTS = MPL/MPK Frelative change of ratio K/L to relative change of MRTS Fimplies the shape of isoquants Fσ = d(K/L)/K/L Ò dMRTS/MRTS Fσ = ∞ for perfectly substituteable inputs Fσ = 0 for perfect complementary inputs Fagain analogy of consumer´s equilibrium Ffirm is limited with its budget Fbudget constraint depends on total firm´s expenditures (total costs – TC), and prices of inputs Ffirm´s budget line (isocost): Ò TC = w.L + r.K, where Ò w…wage rate Ò r…rental (derived from interest rate) F Fif isoquant tangents the isocost: Fif the slope of isoquant equals the slope of isocost... F...if stands: MRTS = w/r , so: FMPL/MPK = w/r Fonly in the above case the firm produces the specific output with minimal total costs, or: F... firm produces maximal output with specific level of total costs E L K L* K* B A firm´s equilibrium In A and B, the firm is not minimizing its total costs In A and B, the firm is not maximizing its total product Q TC1 TC2 Fusually in the case of perfectly substituteable inputs... then... F...firm´s equilibrium as an intersection of isoquant and isocost FMRTS ≠ w/r E L K K* firm´s equilibrium Q TC E L K L* firm´s equilibrium Q TC MRTS < w/r MRTS > w/r Fset of firm´s equilibria upon different levels of total costs (budgets) Fanalogy to consumer´s ICC L K E1 E2 E3 CEP Fset of firm´s equilibria upon different levels of price of one of the inputs Fanalogy to consumer´s PCC E1 E2 E3 PEP L K Fsubstitution effect (SE) – the firm substitutes relatively more costly input with the relatively cheaper one Fproduction effect (PE) – analogy to consumer´s IE – change of price of input leads to the change of real budget L K Q1 Q2 SE PE A TE B C Shift from A to B – substitution effect – total product remains constant (we use Hicks´s approach Shift from B to C – production effect – total product increases Shift from A to C – total effect – the sum of SE and PE TC2 TC1 Fwe compare the relative change of total product and relative change of inputs volume Fdiminishing, constant or increasing Fdiminishing: total product grows slower than the volume of inputs recruited Fconstant: total product and the volume of inputs grow by the same rate Fincreasing: total product grows faster than the volume of inputs recruited Q=10 Q=10 Q=20 Q=30 Q=20 Q=90 Q=10 Q=20 K K K L L L constant – isoquants keep the same distance increasing – isoquants get closer diminsing – isoquants draw apart from each other 1.Linear production function Ò Q = f(K,L) = a.K + b.L Fcontents constant returns to scale: Ò f(t.K,t.L) = a.t.K + b.t.L = t(a.K+b.L) = t.f(K,L) Felasticity of inputs substitution: Ò σ = ∞ → labour and capital are perfect substitutes Ò2. With fixed inputs proportion: Ò Q = min(a.K,b.L) Ò „min“ says that total product is limited with smaller value of one of the inputs – i.e. 1 lory needs 1 driver – if we add second driver, we do not raise the total volume of transported load Fcontents constant returns to scale: Ò f(t.K,t.L) = min(a.t.K,b.t.L) = t.min(a.K,b.L) = t.f(K,L) Felasticity of inputs substitution: Ò σ = 0 → labour and capital are perfect complements Ò3. Cobb-Douglas production function: Ò Q = f(K,L) = A.Ka.Lb Freturns to scale: Ò f(t.K,t.L) = A.(t.K)a(t.L)b = A.ta+b.Ka.Lb = ta+b.f(K,L) Ò depend on the value of “a“ and “b“, if: Ò a+b=1 → constant Ò a+b>1 → increasing Ò a+b<1 → diminishing Q3 Q2 Q1 K K L L K L Q1 Q1 Q2 Q2 Q3 Q3 Linear production funcstion Production function with fixed proportion of inputs Cobb-Douglas production function