Question

Question: The Einstein Bagel Corp. offers a frequent buyer program whereby a consumer receives a stamp each time she purchases one dozen bagels for \(6. After a consumer accrues 10 stamps, she receives one dozen bagels free. This offer is an unlimited offer, valid throughout the year. The manager knows her products are normal goods. Given this information, construct the budget set for a consumer who has \)200 to spend on bagels and other goods throughout the year. Does Einstein’s frequent buyer program have the same effect on the consumption of its bagels that would occur if it simply lowered the price of one dozen bagels by 3 percent? Explain.

Short answer

Answer:

No, Einstein’s frequent buyer program will not have the same effect as the program charges comparatively less price for the same quantity.

Step-by-step solution

Budget Set

The budget set for the consumer is,

$P_{x}X+P_{y}Y⩽200$

Where is the price given for each dozen of bagels.

is the number of dozen of bagels.

is the price of other commodities

in the number of other commodities

Einstein’s Frequent Buyer Program

As given, under this program the consumer buys 10 dozen free. So, eventually, the consumer gets 11 dozen bagels .

So, the amount the consumer can spend on other goods is:

$$\begin{gathered} 60+P_{y}Y⩽200 \\ {P}_{y}Y⩽140 \end{gathered}$$

So, the consumer has $140 left to spend on other commodities.

Lowering the price of each dozens of bagels by 3%

Here, it has been considered that without giving free bagels, the consumers are charged 3% less for every dozens of bagels.

Initial price = $6

New price,

$$\begin{gathered} =6-\frac{3}{100}\times 6 \\ =6-0.18 \\ =5.82 \end{gathered}$$

So, charging a new price, the consumer has to pay for 11 dozen bagels.

Now, the current budget set becomes,

$$\begin{gathered} 64.02+P_{y}Y⩽200 \\ {P}_{y}Y⩽135.98 \end{gathered}$$

Thus, it can be seen that consumers now can spend less amount on other goods. Hence, consumers are more likely to avoid the second program. Therefore, the second program will not have the same effect.