The below mentioned article provides an overview on the Compensated Demand Curve.

The compensated demand curve shows the quantity of a good which a consumer would buy if he is income-compensated for a change in the price of that good. In other words, the compensated demand curve for a good is a curve that shows how much quantity would be purchased at the changed price by the consumer if the income effect is eliminated.

The compensated demand curve can be explained in terms of both the Hicks and Slutsky approaches to the substitution effect. The two-storey Figure 45(A) illustrates the construction of the Hicks and Slutsky compensated demand curves and the uncompensated (or ordinary or Marshallian) demand curve.

The upper portion of the figure shows the substitution effects of the Hicks and Slutsky analyses and the combined price effect.

The lower portion of the figure shows the derivation of the Hicks and Slutsky compensated demand curves and the ordinary demand curve. First consider the lower diagram (B) where the price of good X is taken on the vertical axis. Point P is an arbitrary point on this axis which shows the price of X when the budget line is PQ in the upper diagram. The fall in the price of X as shown by the budget line PQ1 is reflected in point P1 in the lower diagram.

The Marshallian Uncompensated Demand Curve:

First we explain the derivation of the Marshallian uncompensated demand curve. Suppose the initial equilibrium of the consumer is at point R where the budget line PQ is tangent to the indifference curve I1, and OA of good X is bought by the consumer in the tipper diagram.

Let the price of X fall. As a result, the budget line PQ extends to PQ3 and the consumer is at a higher point of equilibrium T on the indifference curve I3 .The movement from R to T is the price effect which includes both the substitution effect and the income effect. This is shown by the D3 curve in the lower portion of the figure. This is the uncompensated (or ordinary or Marshallian) demand curve which shows that when the price of good X falls from P to P1 its quantity demanded increases from OA to OD.

The Hicksian Compensated Demand Curve:

Since the compensated demand curve is based on the substitution effect of a change in the price of good X, we carry the above analysis further and derive the Hicks substitution effect. Let us take away the increase in the real income of the consumer due to the fall in the price of X equal to PM of good Y and Q1 N of X good by drawing a compensated budget line MN parallel to the budget line PQ1.

This line MN is tangent to the original indifference curve I1, at point H. The movement from point R to H on the I1, curve is the substitution effect which traces out the demand curve D1, in the lower portion of the figure when the demand for X increases from OA to OB with the fall in its price from P to P1.

The Slutsky Compensated Demand Curve: