Question

TRUE/FALSE/UNCERTAIN

Suppose a consumer likes Coke just as much as Pepsi and only cares about getting the maximum amount of cola possible. When shopping, this consumer buys only the cola that is cheaper. [Hint: Use a consumer theory diagram in your answer.]

Answer 1

Since the consumer is only concerned about the amount of cola he receives,

Pepsi and Coke are interchangeable here i.e.they are basically Perfect Substitutes.

Let x be amount of pepsi, y be amount of coke

Therefore, the indifference curves of the consumer will be linear with a slope of -1 and the magnitude of the slope =1

That is of the form : U = x+y

Let suppose pepsi is cheaper than coke.

Then the budget constraint of the customer with a budget B will be:

where P is the price of the good x or y as in subscript.

Thus, the slope of the budget line is:

Since pepsi is cheaper, P_x < P_y

Hence, slope > - 1 and the

magnitude of slope is < 1

Thus, the indifference curves will be steeper than the budget line. (on comparing the magnitudes of the slope we get this)

Note that the IC represent the line and not the point. They have been used for labeling purpose only.

It can be seen from this diagram that:

• The axes represent the amount of the pepsi on x axis and coke on y axis.
• AB is the budget line
• The IC represents the various indifference curves steeper than the budget line.
• Now, since there is no IC which is tangent to the budget constraint, the furthest possible IC will be IC₄ for attaining maximum utility
• Any IC further than the IC4 will not touch the budget line at any point which means that any combination of buying goods on that curve is out of budget.Hence, IC4 is chosen
• Hence, the point B will be the point where the consumer gets maximum utility.
• At B, x = OB, y = 0. Thus only pepsi (which is the cheaper good will be bought).
• No coke will be bought.

If however the case was reverse and pepsi was costlier, then the reverse would have happened as shown:

In this case the budget constraint will have magnitude of slope>1 because Px>Py.

The point A is selected and

Only y>0 and x= 0 at point A

Thus in this case only coke is bought.

Conclusion: Only the cheaper good is purchased when the two goods are perfect substitutes = > TRUE.

SideNote: Used Desmos to plot the graphs