Page 100 - DECO405_MANAGERIAL_ECONOMICS

Unit 6: Production Theory

Marginal Rate of Technical Substitution Notes

Marginal Rate of Technical Substitution (MRTS) is the amount by which the quantity of one
input has to be reduced (– x ) when one extra unit of another input is used ( x = 1), so that
2 1
output remains constant (y = y ).

x MP
MRTS(x ,x ) 2 1
1
2
x 1 MP 2
where MP and MP are the marginal products of input 1 and input 2, respectively.
1 2
Along an isoquant, the MRTS shows the rate at which one input (e.g. capital or labour) may be
substituted for another, while maintaining the same level of output. The MRTS can also be seen
as the slope of an isoquant at the point in question.

Isocost Line

If a firm uses only labour and capital, the total cost or expenditure of the firm can be represented
by:
C = wL + rK
where C = total cost
w = wage rate of labour
L = quantity of labour used
r = rental price of capital
K = quantity of capital used
The equation shows that the total cost of the firm (C) is equal to the sum of its expenditures on
labour (wL) and capital (rK). This equation is a general one of the firm's isocost line or equal-cost
line. It shows the various combinations of labour and capital that the firm can hire or rent at a
given total cost.

Example: If C = 900 units, w = 10 units and r = 10 units, the firm could either hire 10 L or
rent 10 K or any combination of L and K shown on isocost line AB in figure. For each unit of
capital the firm gives up, it can hire one additional unit of labour. Thus the slope of the isocost
line is - 1.
By subtracting wL from both sides of the equation above and then dividing by r, we get the
general equation of the isocost line in the following more useful form:
C wL
K
r r
where C/r is the vertical intercept of the isocost line and -w/r is its slope. Thus for C=100 units
and w=r=10 units, the vertical intercept is c/r = 100/10=10K, and the slope is -w/r = -10/10 = -1.
A different total cost by the firm would define a different but parallel isocost line, while different
relative input prices would define an isocost line with a different slope.

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