Page 102 - DECO405_MANAGERIAL_ECONOMICS

Unit 6: Production Theory

OA Notes
Therefore, slope of AB =
OB
Price of X P
= X
Price of Y P
Y
The negative sign indicates negative slope. In absolute terms, the slope of the budget line is
equal to the price ratio of the two inputs.
The budget line of the firm has been superimposed on its isoquant map. The firm would be in
equilibrium at a point where an isoquant is tangent to the budget line AB, i.e., point E. Thus in
equilibrium, the firm produces on the isoquant Q and uses OX units of input X and OY units of
2 1 1
input Y. At point E, the slope of the isoquant Q is equal to the slope of the budget line, i.e., the
2
marginal rate of technical substitution of X and Y is equal to the ratio of prices of two inputs.
MP P
Thus MRTS = X X
XY MP P
Y Y
Thus, to minimise production costs (or to maximise output for a given cost outlay), the extra
output or marginal product spent on labour must be equal to the marginal product per unit
spent on capital.

6.5 Expansion Path

The case of a firm producing 1000 units of output using 10 units of capital and 10 units of labour
(at point a) with input prices w=2 and r=2 is shown in Figure 6.4 using isoquants and isocosts.
Figure 6.4

Thus the cost of this input combination is 40 units. At point a, the 1000 unit isoquant is tangent
to the 40 unit isocost line. If the firm wants to increase its output or expand its production, it will
move to point b if 1500 units are to be produced and then to point c if 1750 units of output are to
be produced. In general, the firm expands by moving from one tangency or efficient production
point to another. These efficient points represent the expansion path.

LOVELY PROFESSIONAL UNIVERSITY 97