The various pairs of the income and the quantity purchased of commodity ‘X’ ((OA1, OX1), (OA1, OX2) and (OA3, OX3)) corresponding to three equilibrium points E1, E2 and E3 are plotted in the lower panel of the Fig. 5.38 to obtain the Engel curve. This Engel curve indicates the relationship between the income level and the quantity of the commodity purchased by the consumer.

Engel Curve and Inferior Goods:

The shape of Engel curve depends upon the shape of income consumption curve (ICC). As discussed earlier, when ICC has a positive slope, the corresponding Engel curve will also have a positive slope.

However, when ICC slopes backward, the Engel curve will have a negative slope. Since commodities generally become inferior after a certain level of income, the income consump­tion curve has a positive slope upto some point. Thereafter, it bends backward.

In Fig. 5.39, the income consumption curve is obtained by joining the points of contact of the budget lines A1B1, A2B2 and A3B3 with indifference curves IC1, IC2 and IC3 respectively. As the level of income rises, the corresponding equilibrium points E1, E2 and E3 represent greater and greater consumption of commodity ‘X’. But, when the level of income further rises, the demand for commodity ‘X’ (being an inferior commodity) falls from OX3 to OX4 and then to OX5. Therefore,

ICC rises upto point E3 and bends backward beyond this point. When various income levels OA1, OA2, OA3, OA4 and OA5 are plotted against the quantities demanded corresponding to equilibrium points (E1, E2, E3, E4 and E5 respectively) on these budget lines in the lower panel diagram of Fig. 5.39, an Engel curve is formed for the inferior commodity ‘X’.

This Engel curve rises upward (positive slope) initially, but bends backward beyond a point. Its shape is again similar to that of the income consumption curve.

Engel Curve and Demand Curve:

A demand curve for a commodity shows how, its demand changes due to changes in its price, assuming other things remain constant. On the other hand. Engle curve indicates how the demand for a commodity changes, when the income of the consumer changes, other things remaining unchanged. The relation between demand curve for commodity ‘X’ and its Engle curve is illustrated in Fig. 5.40.

The upper panel of Fig. 5.40 depicts demand curve for commodity ‘X’. Price of this commodity is shown along the Y-axis and its quantity demanded is taken along the X-axis. The initial demand curve D1D1 corresponds to a level of income I = Y1.

When the income of the consumer rises to I = Y2 and then to I = Y3, the demand curve shifts to the right to D2D2 and then to D3D3. Consequent upon the rise in the income of the consumer, the quantity demanded increases from OX1 to OX2.

Engle curve showing the relationship between income and demand is constructed in Fig. 5.40 by plotting income demand points (OY1 = I1, OX1), (OY2= I2, OX2) and (OY3 = I3, OX3) in the lower panel diagram. In this figure of Engle curve, income is shown along the Y-axis, while quantity demanded of commodity ‘X’ is still shown on the X-axis. This relationship can similarly be shown in case of inferior goods, where Engel curve would be downward sloping.