Question

7. Consider the following table showing the relation between income and quantity demanded for a particular consumer:

            I ($)      10,000             15,000             20,000             25,000             30,000

            Q_x        100                  200                  275                  325                  300

Using the point method, calculate the income elasticity of demand for good X as income rises through the various income levels given above. Also state, at each income level, what type of good is commodity X (i.e. normal-luxury, normal-necessity, or inferior).

Plot the Engel curve. How can you tell from the shape of the Engel curve what type of good is commodity X?

Answer 1

Solution: we will use the formula for income elasticity of demand, which is following

Using this we get results for income levels 10000, 15000, 20000, and 25000 as,

ƞ	Type
0.6	normal necessary
0.904762	normal necessary
1.333333	Normal Luxirious
-2.27273	Inferior

b) This the engel curve for commodity x. It is also telling the same story about the type of good.

X is a necessary normal good as slope of engel curve is less than unit.

X is necessary luxury as where slope is more than 1.

Final slope is negative near the right tail which is saying that now x is an inferior good.