| Summary: | <p> Bullwhip effect in Pricing (BP) refers to the amplified variability of prices in a supply chain. When the amplification takes place from the upstream (i.e. supplier’s side) towards the downstream (i.e. retail side) of a supply chain, this is referred as the Reverse Bullwhip effect in Pricing (RBP). On the other hand, if an absorption in price variability takes place from the upstream towards the downstream of a supply chain, we refer this phenomenon as the Forward Bullwhip effect in Pricing (FBP). </p><p> In this research, we analyze the occurrence of BP in the case of different game structures and supply chain contracts. We consider three game scenarios (e.g. simultaneous, wholesale-leading, and retail-leading) and two supply chain contracts (e.g. buyback and revenue-sharing). We analyze the occurrence of BP for some common demand functions (e.g. log-concave, linear, isoelastic, negative exponential, logarithmic, logit etc.). We consider some common pricing practices such as a fixed-dollar and fixed-percentage markup pricing and the optimal pricing game. </p><p> We discuss the conditions for the occurrence of BP based on the concavity coefficient and the cost-pass-through. We analyze the price variation analytically and then illustrate the results through numerical simulations. We extend the cost-pass-through analysis for a N-stage supply chain and conjecture the BP ratios for a N-stage supply chain. We compute cost-pass-through under both a buyback and a revenue-sharing contract. We compared the BP ratios between a revenue-sharing contract and a no-contract cases. We include both the deterministic and stochastic demand functions with an additive and a multiplicative uncertainty. </p><p> The results indicate that the occurrence of BP depends on the concavity coefficient of the demand functions. For example: RBP occurs for an isoelastic demand, FBP occurs for a linear demand, No BP occurs for a negative exponential demand etc. This study also shows that, FBP and RBP occur in varying magnitude for different types of games and supply chain contracts. The comparison between the stochastic model and the risk-less model shows that the additive or multiplicative uncertainty changes the price fluctuation. The comparison between contract and no-contract cases shows that the contract minimizes FBP or RBP in some cases.</p>
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