The Concept of Economic Efficie^icy 21 



from which he will choose, and a preference map involving the 

 larger number, in principle, could also be inferred.* 



The second element of the problem involves the amount which 

 the consumer budgets for consumption items. This can be shown 

 on a diagram similar to Figure 1, but including a third element — 

 the prices of the two commodities. For example, assume a price 

 for commodity B of Pb and an expenditure budget of M. If the 

 consumer were to spend his entire budget on B, the amount of the 

 commodity which could be purchased would be represented by a 

 distance along the vertical scale, shown on Figure 2 as M/Pi,- 

 Similarly the amount of commodity A which could be bought, were 

 the entire budget allocated to A, would be represented by M/P.„ 

 shown on the horizontal axis. The line connecting the intercepts 

 on the two axes can be called the budget line. It reveals all the 

 various combinations of A and B which can be obtained with a 

 given expenditure, M, given the prices of A, P.^ and B, P^. The 

 slope of the line is determined by the relative prices of A and B, 

 i.e, b/a is equal to Pa/Pb- 



Given his preferences (Figure 1), and his expenditure budget 

 and the prices ruling in the market (Figure 2), how will the con- 

 sumer allocate expenditures between the two commodities so as 

 to maximize his satisfaction? Since indifference curves moving 

 outward from the origin (0) of Figure 3 represent higher levels of 

 satisfaction, the most efficient combination of A and B that can be 

 obtained with a given expenditure is one in which the budget line 

 just reaches an indifference curve as shown by J on Ii. A position 

 on higher indifference curves (L, and I^) is unattainable, given 

 the budget, whereas it would be irrational for the consimier to 

 select a position on lower indifference curves, such as Iq. 



A line tangent to a curve expresses the slope of the curve at that 

 point. It follows then that the slope of the budget line, expressed 

 as the ratio of the prices of A and B (P..,/P,,), is equal to the slo[)e 

 of the indifference curve at the point of tangency---and the sloj^e 

 of the indifference curve, in turn, is expressed as the marginal rate 



* For a generalized statement involving n coniinoditics, a niallicmatical demon- 

 stration can be found in Paid Samiiclson's Foundnlions of Economic Aiidlysis 

 (Cambridge: Harvard University Press, I9,").'5), Chapter \; and Herman Wold 

 and Lars Jureen's Demand Analysis, (New York: John Wiley and Sons, Inc., 

 1953), Chapter iv. 



