Final answer:
The budget set allows the consumer to purchase up to 33 dozens of bagels with $150 considering the frequent buyer program. The program's impact on consumption differs from a 3% price reduction, as it creates a stronger incentive for purchase due to a higher effective discount rate and assuming bagels are normal goods.
Step-by-step explanation:
Constructing the budget set for a consumer with $150 to spend on bagels and other goods throughout the year, considering the Einstein Bagel Corp's frequent buyer program: The consumer receives one free dozen bagels for every 10 dozen purchased.
Each dozen costs $5, so the consumer would need to spend $50 (10 purchases of $5 each) to receive a free dozen. With $150, the consumer could potentially purchase 30 dozen bagels, receiving 3 additional dozens for free due to the frequent buyer program, totaling 33 dozens.
As for the impact of the frequent buyer program on consumption compared to simply reducing the price by 3%, we must analyze the incentive structure. A 3% reduction in price, from $5 to $4.85 per dozen, means minimal savings per purchase.
However, the offer of a free dozen after 10 purchases effectively gives a 9.1% discount (since one out of every 11 dozens is free, and 5/55 is approximately 0.091). Therefore, the frequent buyer program creates a stronger incentive for higher consumption, assuming bagels are normal goods and quantity demanded increases as the price effectively decreases.