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Notes on the Isocost Function and the production decision-making process in economics. It covers the concept of total cost, the equation for the isocost line, and the minimum cost condition. The document also explains how a firm minimizes total cost by selecting a combination of factors where the slope of the isoquant equals the slope of the isocost line.
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The production function summarizes the technologicaloptions facing the firm. Unfortunately it is not enough to bejust aware of these options when making the output and factorinput decision. ¾The^ price^ of a factor of production is extremely importantin this decision. ¾In order to minimize costs and produce efficiently, the firmmust know exactly what its costs will be.
Chapter BJ notes page 4
Capital^0^ C r^1^ C r
Isocost lines (^1 0) C C 0 Labour ww When C, total cost, increases, the isocost line shifts out in aparallel fashion, but the slope of the line does not change.
For a given cost C, the vertical intercepts of theselines are C/r.C/r is the amount of capital that can be employedwhen no labour is used.The slope of the line is -w/r = the negative of thefactor price ratio.When C, total cost, increases, the isocost lineshifts out in a parallel fashion, but the slope
of the line does not change.
The Production Decision We can now determine which combination of factorsproduces a given quantity at the lowest total cost.Capital^2^ C B r^1^ C r^0^ C K^ A^1 r
C^ q^1 (^0 1) C C 0 L 1 ww (^2) C Labour w
“A firm minimizes the total cost of producing a givenquantity by selecting a combination of factors where the slopeof the isoquant equals the slope of the isocost line.” MRTS^ And since^
MPL = − (^) KL , MPK MRTS^ and w^ MP −^ = −= − (^) KL , then^ MPr
wL. rK MP Rearranging w MPL K = (Minimum Cost Condition) r
The firm minimizes the total cost of providing a givenquantity if the ratio of the marginal product of a factor to itsprice is the same for all factors.“The lowest total cost of producing a given quantity occurswhen the ratio of the marginal product of a factors to the lastdollar spent on it is equal for all factors of production.”The rate of the MP
to the price of labour represents theL^ increase in output due to the last dollar spent on labour.To minimize total cost, the additional output due to the lastdollar spent on labour must be equal to the addition outputdue to the last dollar spent on capital.
Capital^1^ C r^0^ C r K^1 K^0
q1q (^0) CC 0 1 (^0) C 0 LL 0 1 w (^1) C Labour w On the diagram, there are two point of tangency of isocostlines with two isoquants.
Expansionpath^ Slope of isocost = -w/r
TotalCost C^1 C^00 q^0
q1Quantity per period “The long-run total cost function shows the lowest total costof producing each quantity when all factors of production arevariable.”
TC=Long-run totalL cost function
The Short-Run Total Cost Function In the short run, one factor is fixed. Hence, the cost of thisfixed factor does not change as quantity produced changes.The short-run total cost function consists of two components:Short-run total cost = total fixed cost + total variable costTC^ = TCS^
(q) =^ F + V(q)S The short-run total cost function shows the lowest total costof producing each quantity when one factor is fixed.The fixed cost must be paid regardless of whether any of thegood is produced. The variable cost will increase when thequantity produced increases.
CapitalCC^2
C^1 K*^
S q^0 q* L*^ L^1
Labour With K* of capital, production of q* units of output with L* units oflabour in the cost minimization production solution.
Minimum cost combinationto produce q0.
The Short-Run Cost Functions of the Firm Fixed Cost : is a cost that does not change with the quantity ofoutput produced. A Sunk Cost:^ a previous expenditure that a firm cannotavoid.The short run total cost function, C
(q) represents the totalS cost of producing each quantity with a given plant size.
Graphing: To derive the short-run total cost function, we can graph totalfixed and total variable costs and then sum them vertically.Cost $
Quantity Next, we can derive the average costs function and the marginalcost function from these curves.
Total Cost^ ‘C(q)’s Total Variable Cost‘V(q)’ Total Fixed Cost^ ‘F’
There are seven cost functions you need to know:The first three we have already discussed.1) Short-run total cost: C
(q)S
(q)S^ C^ MC q qV q ( )^ ( )ΔΔ S ( ) = = Sqq ΔΔ 5) Short-run average cost: AC
(q)S C (q)FAC (q) qq V(q)AFC(q)^ AVC(q)q^ S = =^ +^ S =^ +
