Isoquant and Isocost

I. Isoquant and Isocost (Theory of Production in the long term)
II. Objective: Students will know:
1. Isoquant Curves
2. Isocost Curves
3. Cost minimization or Output maximization; Expansion Path
III. Materials
IV Procedure
1. Isoquant Curves
Isoquant and Isocost curves are used for finding the best level of production in the
long run, when all elements of production are variable, Labor (L) and Capital (K).
Isoquant: A curve showing all possible combinations of inputs capable of
producing a given level of output.
Isoquants are convex







producing a given level of output.
Isoquants are convex to show there is an
increasing cost to replace capital with labor (or replace labor with capital) The
marginal product (MP) of labor decreases as it is used to replace capital.
Marginal Rate of Technical Substitution (MRTS): The rate at which one input is
substituted for another along an isoquant.
MRTS = -∆K
 ∆L
(minus sign is added to make MRTS positive, since the slope of an isoquant is
negative)
The MRTS will equal the ratio of the marginal products of the two units.
The level of output (Q) depends on the use of the two inputs K and L. Since Q is
constant on an isoquant, ∆Q must equal zero for any change in K and L.
To solve for MRTS set ∆Q equal zero
(MPL)(∆L) + (MPK)(∆K) = ∆Q
(MPL)(∆L) = -(MPK)(∆K)
MRTS = -∆K = MPL
 ∆L MPK

2. Isocost Curves
Isocost: Lines that show the various combinations of inputs that may be purchased
for a given level of expenditure at given input prices.
Generally an isocost is a straight line, however there may be a bend in the curve.
For example if a firm receives a discount for a large purchase of capital. (We will
assume the firm has a straight isocost.)
This is an isocost curve for a firm that
must pay $25 for each unit of labor, and $50 for each unit of labor, with a budget
of $400.
The price of Labor is wages (w) and the price of Capital is rent (r). Total Cost (C)
is the sum of the cost of these two inputs
C = wL + rK
The cost function for the above isocost is
400 = 25L + 50K
Then to find the slope of the curve, set the equation equal to capital:
K = C/r - w/r L

K = 400/50 - 25/50 L = 8 – 1/2 L



3. Cost minimization or Output maximization; Expansion Path
Managers whose goal is profit maximization will search for the least cost
combination of inputs
A manager working on
isoquant Q1 is producing 10,000 units, and needs to find the least cost combination
of labor, with a price (w) of $40 and capital with a price (r) of $60 per unit.
The firms starting point is A, using 60 units of labor, and 100 of capital. Total cost
at that point is $8,400
C = wL + rK = ($40 x 60) + ($60 x 100) = $8,400
Now if the manager reduced capital to 60 and increased labor to 90 the firm would
be move to point B.
C = wL + rK = ($40 x 90) + ($60 x 60) = $7,200
The firm has kept the same level of production while reducing costs. But what if
the manager thought the firm might do even better with only 40 units of capital and
150 units of labor (point C)?
C = wL + rK = ($40 x 150) + ($60 x 40) = $8,400
The firm moved back to the original isocost curve, and the price of inputs
increased. The firm is best of on point B.
The firm could also take a marginal product approach to cost minimization. Since:
MRTS = MPL/MPK = w/r

MPL/w = MPK/r











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