Model Setup. We begin by describing a P4D deal from the US which serves as a motivating example of the stylized model described below. Shire Pharmaceuticals introduced an extended release version of its ADHD drug called Adderall XR in 2001. Under the Xxxxx-Xxxxxx terms it had exclusivity until April 2005 (initial exclusivity was until October 2004, but then had received pediatric extensions). The underlying patents for the extended release version, unless invalidated, were effective until 2018. In November 2002, Xxxx laboratories filed an abbreviated new drug application (ANDA) which was followed by a second filing by IMPAX in November 2003. Patent litigation ensued, but Xxxxx settled with both parties before any court outcome. Shire settled with IMPAX (the second filer) to enter the market no later than December 2010, but with a non-exclusive license. It also settled with Xxxx laboratories (the first filer), which acknowledged that Shire’s patents were valid and to agreed to delay entry until April 1, 2009. At that point, Xxxx would enter with a 180-day exclusive licence from Shire and pay royalties as a proportion of its profits from the sales of generic Adderall XR over the exclusivity period [Xxxx Laboratories, Inc., 2006]. Per the terms of the agreement, Xxxx would also be allowed to enter earlier if another party were to launch a generic version of the drug. Similarly, Teva (which had acquired Xxxx laboratories in the meantime) started marketing generic version of Adderall XR in the US on April 2, 2009, and six months later IMPAX also entered the market. For a discussion on side payments and additional examples, see Xxxxxxxx [2007]. Further details of patent litigation and market entry rules in the US and EU are given in section 3 and our model is based on these institutional details. We propose a dynamic game Γ with J +1 players that illustrates the essential elements of interactions between a brand name firm B (player 0), which is protected by a patent, and J ≥ 1 potential generic challengers (G1, . . . , GJ ). As in Xxxxxxxx and Xxxxxxx [2007], our game unfolds in the shadow of a trial. Our stylized game is designed to capture the market authorization rules and main features of P4D cases described earlier and stylized below.
Model Setup. For this study, the Southeast Florida (SEFL) Regional STOPS model developed in 2016 by AECOM and Connetics Transportation Group (CTG) was adopted. The model covers Palm Beach, Broward, and Miami-Dade Counties. As part of this effort, the team developed a user interface to automate the preparation of certain STOPS input files for any fixed-guideway transit project in the tri-county region. The model was calibrated to base year 2015, which had a total of 504,119 unlinked trips in the study area. The package provides all the required input files readily available, including the CTPP and census files, regional SED forecast files and highway skims, and GTFS files. Figure 5 provides a list of input files. Figure 5 Input files for STOPS.
Model Setup. For the purpose of this study we use the latest version of TBEST (4.4), which was developed and upgraded by the State of Florida Department of Transportation (FDOT) in 2016. The software is available for download at xxx.xxxxx.xxx. We use the latest update on the socioeconomic data package that includes the 2014 American Community Survey 5-Year Estimates, the 2014 InfoUSA Employment data, and the 2015 Florida Department of Revenue Parcel-level Land Use. The software also employs the TBEST 2016 Land use model with default control parameter values (including bus capacity = 40 seats, a market capture buffer distance of 0.25 mile, etc.) and default service level attributes (i.e. no changes implied in headways, number of arrivals, park-n-ride parking capacities, etc.). Furthermore, in order to comply with STOPS results, the model is run for year 2015 (i.e. no growth rates are set). TBEST provides a user friendly graphical interface which interoperates with ESRI ArcGIS software. The unit of analysis in TBEST is a transit system, which comprises its extent (i.e., what counties are included), parcel data, and imported routes from the GTFS files. Within the software environment, the user can easily manipulate any of the socio-demographics, route-level attributes, stop-level characteristics, or transit service patterns in order to evaluate different scenarios (Figure 6).
Model Setup. We propose a dynamic game Γ with J +1 players that illustrates the essential elements of interactions between a brand name firm B (player 1) which is protected by a patent and J ≥ 1 potential generic challengers (G1, . . . , GJ ). Our game is designed to capture the market authorization rules and main features of P2D cases described earlier and stylized below.
Model Setup. We consider an inventory supply chain system in which a supplier manages the supply of a single product for the retailer. The demand at each period (dt) is stochastic, independent, and identically distributed (i.i.d.) with mean λ and standard deviation σ. We consider the case where the SLA outlines: • The length of the performance review period (T ) • The amount and type (lump-sum or linear) of penalty and bonus • The lower target service level (i.e., penalty threshold) – when the supplier performs below this target in a performance review period, a financial penalty (lump-sum or linear) is applied to the supplier • The upper target service level (i.e., bonus threshold) – when the supplier performs above this target in a performance review period, a financial bonus is paid to the supplier The supplier replenishes the inventory at the beginning of the inventory review period t to St to satisfy the demand of period t. Then the retailer's demand is observed, and the unmet demand is backordered. The supplier does not incur the backorder (shortage) cost; thus, this cost is not directly included in our model. However, the retailer incorporates this cost into the contract by setting the target service level and penalty structures. We assume that excess inventory at the end of the period is discarded (Xxxxxxxxxx, 1989; Xxxx & Xxxxx, 2013; C¸ etinkaya & Xxxxxx, 2010; Xxxxxx, 2007; Xxx, Xxxx, Xxxxxxxx, Xxxx, & Xxxxx, 2011). Since the end of the period is discarded, the unit holding cost in our model is composed of the unit storing cost plus the unit purchase price and the unit disposal cost minus the unit salvage value. There is a constant unit inventory holding cost h per item held at the end of each inventory review period. The supplier uses a periodic-review base-stock policy with replenishment. The supplier makes a decision on the base-stock at each inventory review period based on the demand distribution and the current service-level performance. Therefore, at the beginning of period t, the supplier determines the stocking level and places an order. Here we consider an inventory setting of a supply chain with zero lead-time, similarly to Xxxxxx (2005) and Xxxxxx et al. (2018). We consider both static and dynamic inventory policies and study a supplier's problem under an optimal contract. Figure 1 illustrates the problem setting.
Model Setup. Similar to Xxxxxxxxxxxxx and Rysman (2009), I consider the following consumer level in- finite horizon dynamic optimization problem with a discount factor b. At each time period t (month in this case), each consumer i chooses either one of the currently available products, Jt , or chooses to defer purchase to a future period and continue to use the currently owned car or avail of other mode of transportation. Similarly, at period t + 1, the consumer chooses one of the Jt+1 products or opts for the outside option j = 0 so that she maximizes the sum of the expected discounted value of utilities conditional on her information at period t. Each product j ∈ Jt is characterized by observed characteristics x jt (e.g. manufacturer, size, reliability, etc.), the unobserved (by the econometrician) characteristic ξ jt , and the price p jt . Extending Xxxxxxxxxxxxx and Xxxxxx (2009), I assume that products deterministically de- preciate at a rate of x .0 I assume that consumers are heterogeneous in their taste for product characteristics, price sensitivity and willingness to travel. To model this, I define consumer- specific random coefficients αi = (αx, αp, αd ) for car characteristics, price, and distance to the dealer, respectively. Following the literature, I assume that consumers are completely informed about all time t related information when making decisions at time t. Moreover, consumers have idiosyncratic shocks to their preferences for each product and in each period εi jt , which I assume as being i.i.d. across (i, j, t).7 Following the random coefficients discrete choice framework of Xxxxx et al. (1995), con- sumer i obtains the following one-period utilities for each available choice at time period t: 6λ is currently assumed to be the same across all cars. However, this can be relaxed to allow brand-varying depreciation rates. 7Logit errors (and most i.i.d error terms) typically imply unrealistic welfare gains from new products (see Xxxxxx 2002). Xxxxxxxxx and Xxxxxx (2005) argue that this feature of the logit-based demand model make them inappropriate in contexts where consumers face a vastly different numbers of products over time. Xxxxxxxxx and Rysman recommend addressing this problem by including the log of the number of products, ln(Jt ), as a regressor. A coefficient of 0 on the associated parameter implies the logit model is well specified, whereas a coefficient of -1 implies “full crowding," so there is no demand expansion effect from increasing...
