• the Marginal Rate of  Substitution (MRS = MU_y/MU_x) equals the slope of the Budget Line = Δy/Δx;

• the MRS also equals negative of price ratio - (P_x/P_y); and,

•  MU_x/P_x = MU_y/P_y.

2.Manipulations
   From the basic analytic mechanism of the indifference curve and budget line a range of additional information can be deduced including the:
    a) Income-Consumption Curve;
    b) Engel Curve;
    c) Price Consumption Curve; and,
    d) Demand Curve.

a) Income-Consumption Curve
    An increase in income increases the intercepts of the budget line but leaves its slope constant - assuming constant prices.  The locus of tangents of budget lines with indifference curves forms the income-consumption curve or the set of commodity combinations (x, y) purchased as income increases - assuming constant prices and taste (M&Y 10th Fig. 4.1a; M&Y 11th Fig. 3.1a;B&Z Fig. 3.14; B&B Fig. 5.2; B&B Fig. 5.3).   If prices change so does the income-consumption curve (M&Y 10th Fig. 4.1b; M&Y 11th Fig. 3.1b; B&Z not displayed; B&B not displayed).

b) Engel Curve
    The amount of a commodity (x) purchased at different levels of income can be derived from the income-consumption curve (M&Y 10th Fig. 4.2; M&Y 11th Fig. 3.2; B&Z Fig. 3.14) to form  Engel curve (M&Y Fig. 4.2, p. 92; B&Z not displayed; B&B Fig. 5.3).  The Engel curve plots changes in the level of X consumed (x-axis) against changes in money income (I on the y-axis).  The shape of an Engel curve depends on the type of commodity and consumer taste - assuming constant prices.  The quantity of a commodity (x) purchased will increase at either an increasing or decreasing rate as income rises - depending on the type of commodity (M&Y 10th Fig 4.3a & 4.3b; M&Y 11th Fig. 3.4a & 3.4b; B&Z not displayed; B&B Fig. 5.4).  The Engel curve can be useful in marketing research as it will indicate the path of demand for a given commodity as income increases (or decreases).

c) Price-Consumption Curve
    If the price of one commodity (x) changes a new set of combinations (x, y) is created between the changing tangents of the budget line and indifference curves forming  a price-consumption curve for the commodity (x) - assuming constant income and prices of the other commodity (y) (M&Y10th  Fig. 4.4; M&Y 11th Fig. 3.6; B&Z Fig. 3.14; B&B Fig. 5.1).  The price-consumption curve shows how much of a commodity (x) is purchased if its price changes - assuming constant income and constant prices for the other good (y).

d) Demand Curve
    The demand curve for a given commodity (x) can be derived from the price-consumption curve showing how much of that commodity (x) is purchased at different prices - assuming constant income and constant prices for the other good (y) (M&Y 10th Fig. 4.5; M&Y 11th Fig. 3.7; B&Z Fig. 4.1; B&B Fig. 5.1). The shape of the demand curve (x) depends on taste, income and the type of commodity - assuming constant prices for the other good (y).  Note that the demand curve is plotted with the quantity of x on the x-axis and Px on the y-axis.  For normal goods the demand curve is downward sloping from the left reflecting the basic Law of Demand: the lower the price, the greater the demand.

3. Consumer Surplus & Price Indices

a) Consumer Surplus

Consumer surplus is the difference between the maximum a consumer is willing to pay for a total quantity of a commodity (x ) and what the consumer actually pays (M&Y 10th Fig. 4.9; M&Y 11th Fig. 3.12; B&Z Fig. 4.8; B&B Fig. 5.14).  

It is critically important to appreciate that the demand curve reflects 'willingness to pay'.  Thus to get quantity C, a consumer is willing to pay P.  However, the consumer would have been willing to pay a higher price to get a smaller quantity.  In effect, a consumer gains a bonus or a surplus because at P he or she gets that smaller quantity (plus much more) and at a lower price.

Accordingly, as price rises or falls the consumer surplus changes (M&Y 10th Fig. 4.10; M&Y 11th Fig. 3.13; B&Z Fig. 4.10; B&B Fig 5.15).  Similarly, the size of the consumer surplus will vary according to the shape of the demand curve - the gentler the slope, the greater the consumer surplus (M&Y 10th Fig. 4.11; M&Y 11th Fig. 3.15; B&Z not displayed; B&B not displayed).

b) Price Indices

A consumer price index measures the combined income effect of price changes of given commodity combination (x, y).  It measures how much income must increase or decrease to purchase the same commodity combination (x, y) at different price levels - through time (M&Y 10th Fig. 4.13; M&Y 11th Fig. 3.17; B&Z not displayed; B&B Fig. 5.20).

If combination Q_x + Q_y cost $100 in year 1 but cost $110 in year 2 then, in effect income would have to increase 10% if the consumer was to purchase the same fixed quantities of x and y in year 2.  If income did not increase by 10% then the utility or satisfaction of the consumer would decline.  The increased cost of the same basket of goods and services is a measure of price inflation.

In Canada the Consumer Price Index (CPI) is the usual measure of consumer price inflation.  A typical or standard basket of goods and services purchased by Canadians is determined during the Census (say in the year 2001).  The price of this basket is also estimated for that year.  In subsequent years the cost of the standard basket is estimated.  The degree to which the cost increases for the same basket of goods and services provides the estimated consumer inflation rate.  If consumers are to simply maintain their level of utility then income must increase by at least the same rate as the CPI.

There are, however, inherent problems with the CPI and all 'price indices' (pp. 117-118).  Such problems include:

a) substitution bias: consumers will tend to substitute less expensive for more expensive goods and services, i.e. if the price of a commodity included in the basket goes up, consumers may shift to less expensive goods included or not included in the basket.  Either way the CPI tends to overestimate price inflation;

b) quality changes: overtime the quality of some goods and services increase.  If prices stay constant consumers are better if than the CPI would indicate; if their prices go up, consumers may still be as well off because the commodity is better.  Examples include automobiles.  Twenty years ago it was unheard of for consumer to receive a 10 year 100,000 km warranty simply because the quality of the vehicles at that time would not support such a guarantee.  Cost may go up but if quality also rise the CPI may overestimate inflation;

c) new products: twenty years ago there were no personal computers as we know them today; there were no DVDs or CDs.  Such new products may enter the typical consumer's purchasing pattern yet not be reflected in the CPI; and,

d) changing shopping habits: if consumers shift from high-end specialty or department stores to low-priced 'big box' stores like Walmart reduced prices would indicate that inflation is lower but the quality of service may also be less.