Chapter 6, Problem 1DQ

To determine

Graphically illustrate the effect of a compensated change in the price of nuts.

Explanation of Solution

Figure 1 illustrates the effect of a compensated change in the price of nuts.

In Figure 1, the vertical axis measures the bolts and the horizontal axis measures the nuts. If T initially maximizes the utility by consuming Bundle A on budget line L1, then the price of nuts reduces and that causes to move the budget line to L2. A compensated price change, that is change in price and change in income, which together leaves the well-being of the consumer unaffected. Hence, to reflect the changes in price, the compensated budget line has the slope of the new budget line (L2). It will only be tangent to the original indifference curve to indicate unaffected well-being. The bundle that is purchased by T with the compensated price change is the bundle where the compensated budget line is tangent to the initial indifference curve.

As the given two goods are ideal complements, a price change will affect the quantity of nuts and bolts in equal amounts. The nuts’ price reduction would allow T to achieve a higher utility rate with the same amount of income. Although, once the price change is offset, the consumption of nuts and bolts will not change. Also, as the nuts and bolts are perfect complements, they can tend to be consumed in the same proportion.

The effect of compensated price change on consumption is called the substitution effect of a price change. This substitution effect has a movement along an indifference curve to a point where the slope of the indifference curve equals to the slope of the new budget line.  There is no substitution effect because the compensated budget line is tangent to the original indifference curve at the same consumption bundle as the original budget line.