Showing Wealth and Substitution Effects A Primer

Overview Graphing wealth and substitution effects is one of the trickiest parts of microeconomics. This presentation will walk you through a 5 step process that should help minimize mistakes. We will begin with a basic discussion of the two effects, and then move on to demonstrating how to show them on a graph.

Overview: The Substitution Effect When the price of a good changes, there are two impacts on the consumer. First, the price of one good relative to the other has changed. Second, the change in price changes the overall purchasing power of a dollar. The substitution effect is the change in what is consumed that is due to the change in relative prices. It is important to realize that the substitution effect for a good is always in the same direction as the change in relative price; that is, if the price of good x relative to good y goes up, the substitution effect will always be to consume less x and more y. It does not matter whether x and y are normal or inferior goods. If x gets more expensive in terms of y, the substitution effect is negative.

Overview: The Wealth Effect The other effect from a price change is a change in overall wealth, or purchasing power. When the price of any good goes down, bundles of both goods that were previously too expensive become affordable. Similarly, when the price of any good goes up, many bundles that were previously affordable are now too expensive. What has happened is that a dollar now buys more or less. Since we care about what dollars can purchase, and not about the dollars themselves, we say that the consumers wealth has changed, as they can now consume more or less of both goods. This change in wealth will cause a change in consumption of both goods, and the direction of the change will depend on whether the particular good is normal or inferior. Putting the substitution and wealth effects together will show the total change in consumption from the price shift.

Graphing the Changes: Our Starting Point Everything that is to follow is based on the following formula: Px ___ Py = MUx MUy ______

Graphing the Changes: Our Ending Point Ultimately, our goal is to show the change in consumption when prices change, broken into substitution and wealth effects. We will proceed in 5 steps. A C B

Step 1: Find the Initial Optimum You should always begin by graphing the initial budget constraint and labeling the axis and intercepts. Then, show the initial consumption bundle, and draw an indifference curve that is tangent to the budget constraint at the initial consumption bundle. Mark the initial consumption bundle as point A. Generally, you can pick any point you want on the budget constraint that isn’t one of the intercepts, but it will be easier if you pick something in the middle.

Step 1: Find the Initial Optimum A X Y M/Py M/Px BC old IC 1

Step 2: Draw the New Budget Constraint The next step is to draw the new budget constraint. You will be told which price is changing, and whether it is increasing or decreasing. Remember that the new budget constraint should share one intercept with the old one, the intercept for the good whose price did not change. In our example, the price of good X has decreased, and X & Y are both normal goods.

Step 2: Draw the New Budget Constraint A X Y M/Px M/Px’ M/Py IC 1 BC old BC new

Step 3: Draw Imaginary Budget Constraint Now comes the tricky part. The next step is to draw another budget constraint that is parallel to the new budget constraint, and tangent to the indifference curve. Then, mark the point of tangency as point B. The change in consumption from A to B is the substitution effect. It is the unique consumption bundle that is just as good as the original consumption bundle, but that has MUx/MUy equal to the new price ratio. If you are having trouble, you can use arrows to identify the area where B needs to be relative to A. Keep in mind that one quantity needs to increase from A to B and the other needs to decrease. If both X and Y are higher or both X and Y are lower at B relative to A, something is wrong!

Step 3: Draw the Imaginary Budget Constraint A X Y M/Px’ B Note that X increased here relative to A, while Y decreased. M/Py M/Px IC 1 BC old BC new BC I

Step 4: Find New Optimum Now we need to find the new optimal bundle on the new budget constraint. Here, we need to use our information about which good (if any) is inferior. What we will do is mark a new bundle C on the new budget constraint, using the following facts: If the price of any good has increased, wealth has gone down. If the price of any good has decreased, wealth has gone up. Consumption of a normal good moves in the same direction as wealth. Consumption of an inferior good moves in the opposite direction of wealth. If the price of a good has increased, consumption of the good must decrease. If the price of a good has decreased, consumption of the good must increase. These facts tell us where the new bundle C must be relative to bundles A and B. The first four tell us where C needs to be relative to B, the last two where C needs to be relative to A. Facts 5 and 6 are only relevant when there is an inferior good, and the inferior good’s price changed. Here are some examples:

Step 4: Find New Optimum X&Y are normal, Py has increased Consumption of Y must decrease from A to B, and from B to C Consumption of X must increase from A to B, decrease from B to C Consumption of Y must decrease from A to C X is inferior, Py has increased Consumption of X must increase from A to B, and from B to C Consumption of Y must decrease from A to B and from B to C Y is inferior, Py has decreased Consumption of Y must increase from A to B, decrease from B to C Consumption of X must decrease from A to B, increase from B to C Consumption of Y must increase from A to C. This is from fact #6.

Step 4: Find New Optimum Using the listed facts, we can draw arrows to guide us to where C needs to be. For example, fact 2 tells us that in our example, since Px has gone down, wealth has gone up. Fact 3 then tells us that consumption of X & Y must go up. Thus, we now know that relative to bundle B, bundle C must have higher consumption of X & Y. Since X & Y are both normal, we don’t need to worry about facts 5 or 6. Now, we just need to draw arrows starting at point B that extend to the new budget constraint to see the region that must contain point C. When you have placed bundle C, make sure to draw a new indifference curve.

Step 4: Find New Optimum A X Y M/Px’ B C M/Py M/Px IC 1 IC 2 BC old BC new BC I

Step 5: Show SE and IE Last, we need to show the substitution effect, the income effect, and the total effect. This can be done by writing something like “Substitution effect is from A to B”.

Step 5: Find New Optimum A X Y M/Px M/Px’ B C Substitution Effect is A to B Income Effect is B to C Total Effect is A to C M/Py IC 1 IC 2 BC old BC new BC I