A grocery store wishes to attract more customers and is considering starting a promotion. The supermarket could give a discount on some frequently purchased items or a general discount. The store manager asks you to study which discount would raise potential customers' welfare the most. Store data show that the typical customer has a weekly budget of$120 and buys ten units of frequently purchased items at unit price of $6 and six units of less frequently purchased items at a unit price of $10. The data also shows that all the items the store sells are normal goods.
1. In a diagram, draw the budget constraint of the typical consumer. Measure frequently purchased items along the horizontal axis
First you assume that the typical customer considers frequently purchased items an imperfect substitute to less frequently purchased items.
2. In your diagram, add an indifference curve to illustrate the optimal bundle of the typical customer Suppose the store gave a $2 dollar discount on frequently purchased items.
3. In your diagram, show how the discount would affect the budget constraint of the typical customer.
4. Along this new budget constraint, pick a reasonable new optimal bundle.
5. You cannot exactly tell what combination the store customers would buy once offered the discount, however explain to the store manager that with the information you have you can tell they will certainly buy more of frequently purchased items. In the diagram, from the new optimal bundle draw a vertical segment to highlight the distance between the new and old budget constraints at this quantity of frequently purchased items. This distance illustrates the cost per customer of the discount program measured in units of less frequently purchased items (if you multiply the distance by the unit price of less frequently purchased items ($10) you find the monetary cost per customer of the discount program) Suppose instead, the store gave each customer a voucher for the amount you found in part f. Customers could spend the voucher on any store item.
6. In your graph, show the budget constraint of the typical customer after he receives the store voucher.
7. In your graph, show that customers would rather receive the voucher than the discount on frequently purchased items even if the two promotions cost the store the same amount.