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Unformatted text preview: © 2011  Steven Tschantz Supply chain pricing model Steven Tschantz 3/15/11 Problem A manufacturer rarely sells directly to consumers. Many products are sold by neighborhood retailers who purchase wholesale from manufacturers. Imagine a simple case where a manufacturer sells a unique product to retailers at a uniform price, each retailer essentially a local monopoly seller. How does the manufacturer set wholesale price, and given a wholesale price, how does the retailer set the retail price the final consumers see? What would happen if the manufacturer could bypass the retailer and sell directly to the consumers? Model The manufacturer computes an optimal profit maximizing wholesale price, his markup over marginal cost, and then the retailer adds his own markup over the wholesale price plus his own marginal costs to get a final retail price to consumers. The prob lem with separate wholesale and retail operations is that the retailer is including a retail markup on the markup of the manufac turer, the two firms in the supply chain are each extracting a profit, the final price to the consumers is that much higher and the quantity sold is less, with the result that there is less total profit made by the manufacturer and retailer together than if a single monopolist sold to consumers. This is known to economists as the double marginalization problem. To be sure, there are other efficiencies of such a supply chain, practical constraints on alternatives, negotiations between manufacturers and retail ers, volume discounts and other schemes for avoiding the worst consequences of this problem. But it is worth considering the pure version of this problem first in order to evaluate these other considerations. There are two prices for the product to be determined, the wholesale price p w , set by the manufacturer, and the retail price p r , set by the retailer. The manufacturer faces some marginal cost mc w of production and the retailer will likely face additional marginal costs mc r , over the wholesale price the it pays. Consumers see the retail price and buy some quantity from the retailer as a function of retail price q r H p r L . The retailer must buy this same quantity from the manufacturer at the wholesale price. The retailer makes a profit over fixed costs on this product of P r = q r H p r L H p r H p w + mc r LL , choosing the price p r that maximizes this profit. The manufacturer makes a profit selling through this retailer of P w = q r H p r L H p w mc w L = q w H p w L H p w mc w L where we may think of the retailer's optimal price p r = p r H p w L as being given as a function of the wholesale price and define q w H p w L = q r H p r H p w LL the effective wholesale demand through this retailer as a function of the wholesale price. Each different retailer could face a different demand, at the least because they serve different local populations. If the demands retailers face are in proportion, say to their local populations, then the profit maximizinglocal populations....
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This document was uploaded on 10/28/2011 for the course MATH 256 at Vanderbilt.
 Spring '11
 Schantz
 Math

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