Wanda's Emporium (WE) is a Midwestern retailer with a strong reputation for selling good- quality merchandise at an affordable price. Part of the company's value promotion lies in its simple pricing strategy of charging a single fixed price with no promotions or discounts. However, the continuous growth of e-commerce is threatening this business model and the company is considering the possibility of using discount coupons sent in emails particularly to online shoppers to stimulate demand.

You have been hired to help the company explore this possibility. As a first step, you will conduct a pilot test on a specific category of T-shirts. This is a seasonal category with a four-month selling season and an initial inventory of 10,000 units. Based on some historical data that you have collected, you have estimated that the total market potential for this product is 16,000 customers and that the average willingness-to-pay of a customer in this population is uniformly distributed in the range [$0,$25].

(a) Using this information, estimate a linear demand function for T-shirts as a function of price, i.e., a demand function of the form D(p) = A B p. What are the values of A and B?

(b) Using the linear demand function in part (a), what would be the optimal fixed price that the company should charge? How many units should the company expect to sell? What are the company's revenues under this fixed price policy? What is the marginal value of an extra unit of inventory. (Assume no salvage value for unsold units.)

The company is considering emailing a discount coupon to all of its customers that can be redeemed online or in the store. You need to determine an optimal strategy, that is, what is the optimal retail price ($p) to charge for the product and what is the discount price ($pc) to offer to those customers who end up redeeming the coupon. (In practice, pc = (1d)p, where d is the percentage discount offer on the coupon, for example, d = 20% discount.)

(c) Based on some preliminary data, you have estimated that only consumers with a willingness- to-pay below $10 will respond to promotional coupons (i.e, customers with a valuation above $10 will not redeem their coupons). This allows you to segment the population of consumers into two groups: coupon-Sensitive (S) and coupon-Insensitive (I) customers. For each of these two groups estimate a linear demand function of the form:

DS(pc) = AS BS pc for 0 pc $10 DI(p)=AI BIp for$10p$25.

What are the values of AS, BS, AI and BI?

(d) Under this condition, what is the optimal retail price (p) to charge for the product and what is the optimal discount (d) to offer on the coupons (as a % of the retail price)? What are the revenues in this case? What is the marginal value of an extra unit of inventory.

Hoping for help with c and d--thanks!