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Dr. Barry Haworth

University of Louisville

Department of Economics

Economics 301

Substitution and Income Effects in the Indifference Curve model

Homer Simpson, our representative consumer, consumes varying amounts of beer and pork rinds. Assume that B = quantity of beer consumed, and that R = quantity of pork rinds consumed. Homer’s utility function is given as:

The marginal rate of substitution (which is the slope of Homer’s indifference curve) between beer and pork rinds is given in absolute value as:

Recall that this can be derived from Homer’s utility function. If we use a different utility function, then we get a different MRSR,B. Assume further that the price of beer is $4, the price of pork rinds is $2, and that Homer’s income is $200. We can obtain Homer’s budget constraint from this information, which we can rearrange as:

B = -0.5R + 50.

A consumer equilibrium occurs in the graph below at pt. X1, where the (blue) indifference curve is tangent to the (red) budget constraint.

It is possible to calculate the quantities of beer and pork rinds at this consumer equilibrium. After doing so, we would find that B* = 25 units and R* = 50 units.

How is the graph above affected when the price of pork rinds increases from $2 to $4? This change is shown on the graph below. The budget constraint becomes steeper and Homer moves to a new (pink) indifference curve and a lower level of utility at pt. X2. If we calculate the new consumer equilibrium at pt. X2, we would get B* = 25 and R* = 25.

Notice, however, that the price change included two actions. The movement from pt. X1 to pt. X2 involved a change in the marginal rate of substitution (i.e. a change in the slope of the indifference curve), and a change in utility (i.e. a change from the blue indifference curve to the pink indifference curve). This is different from a change in income, which only involves one change – a change in utility. These two actions form the analytical basis for...