Compensated Demand Curve:
Compensated demand function for a commodity (say x1) of an individual consumer represents demand quantity for that good (which is purchased by the consumer) as a function of price of that good and prices of other goods under constant real income and constant other things.
Notationaly, it is given by x1=x1(p1, p2, y),
where y is the real income. Demand curve for a good showing the relationship between demand quantity for that good and its own price given other things and given real income is known as compensated demand curve along which real income is constant (real income is defined by the ratio between money income and price level). Along the demand curve price of that good changes, so money income should be proportionately adjusted or compensated such that real income is constant. That is why the corresponding demand function and demand curve is known as compensated demand function and compensated demand curve.
There are two different approaches to the measurement of real income, viz.,
• Hicksian Approach: In Hicksian approach, real income is measured in forms of utility. A constant real income means a constant utility. Thus, demand quantity for a good purchased by a consumer as a function of prices of all goods under constant utility and constant other things is known as compensated Hicksian demand function.
Demand curve for a commodity showing the relationship between quantity demand for that commodity and it's own price under constant other things and constant real income in terms of utility is known as compensated Hicksian demand curve.
• Slutsky's Approach: In this approach, real income is measured in terms of purchasing power. A constant real income means a constant purchasing power (it is denoted by yp). Demand quantity for a good purchased by a consumer as a function of prices of all goods under constant other things and constant purchasing power is known as compensated Slutsky's demand function and corresponding demand curve is known as compensated Slutsky's demand curve.