Pasos para realizar la evaluación de Seguridades

In Stage I of the game, firms adjust their product portfolios. In particular, managers need to decide which new products to introduce, and which existing products to take down, to maximize expected portfolio profits. Forward-looking firms in fast-changing high-tech

markets anticipate not only Stage II static profitspf mt(Jmt), but also lifetime profits of their

new productsEP_jm(Jmt)in the market:

Pf mt= max Jf mt✓Jf,t_{j2Jf mt}

Â

_{,j2Jf m,t 1} ⇥ Epjmt(Jmt) Fjmt⇤+

Â

j2Jf mt,j2/Jf m,t 1 ⇥ EP_jm(J_mt) SCjmt⇤, (1.3.6)

where SCjmt is the sunk introduction cost of product j to market m in month t, reflect-

ing one-time marketing costs, product launch events, renegotiation with local retailers,

etc.; F_jmt is a monthly fixed cost to maintain a product in the firm’s portfolio, reflecting

any channel fixed costs and per-period marketing costs (billboards, TV airtime rates, etc.). Therefore, the first term is the expected total static profits of maintaining existing products, and the second term is the expected lifetime profits of introducing new products.

This specification of firms’ objective function, rather than a Bellman equation, makes several important simplifying assumptions. First, I assume zero scrap values—if a product

is taken down, firms make zero profits56_{. I then interpret firms’ product discontinuation}

decisions as static57_{, which allows me to identify maintenance costs}58_{. Firms therefore}

evaluate only the product’s static profits—as well as its static impact on other products in the portfolio if it is maintained on the shelf—against the maintenance cost. Second, I

interpret the sunk introduction costsSCjmt’s to also include opportunity costs of waiting

56_{This is reasonable, given the lack of capacity (see Section1.2) and liquidity (major manufacturers are}

mostly large multi-sector firms) constraints in this market.

57_{The static assumption here is also based on managers’ practice in this industry: Once a product is intro-}

duced, they do not actively think about its life cycle, but only monitor sales so that its presence in the market is always justified. This is reasonable, in the sense that the impact of any single product’s introduction on other products’ life cycle paths is likely second order compared to its static impacts.

to launch the product in the future. The opportunity costs are likely small in this market, given the fast-changing technology—an available design today will quickly become obso- lete in a few months. As a result, the dynamic game of product introductions collapses to

equation (1.3.6), where firms weigh expected lifetime profits of a new product against its

sunk introduction cost.

However, as alluded to earlier, the expectation of future sales of a product,EP_jm(J_mt),

taken over the future evolution of technologymcjmt’s, and product portfolioJmt’s, requires

managers to keep track of trillions of states, and is thus intractable. While I have shown in

Section1.2that the static observables have predictive power for future sales of a product,

and thus can be used by managers in new product introduction, the question of what managers actually do in the industry remains.

Is the concept of the product life cycle and the prediction of its magnitude used by

managers in this industry? This was Theodore Levitt’s concern (Levitt, 1965)59_{. Since}

then the concept of the product life cycle has been written into an abundance of business

review articles60_{and introductory marketing textbooks}61_{, and has become one of the most}

familiar concepts among executives around the world. Interviews with product managers of smartphone manufacturers and industry analysts in China suggest the prevalent use of the product life cycle to forecast product sales after introduction. For example, the Head Product Manager of Samsung Mobile in China said:

Every month we determine PLCs and EOPs [end-of-products] to adjust our product lines. Everyone tries their best to make predictions of PLCs given the competition. We used to be able to sell our mid-level handsets for 18 months, but can barely maintain 12 months now with the amount of com- petition.

Combined with the descriptive evidence shown in Section 1.2, I model firms’ prod-

uct introduction decisions by weighing a product’s sunk cost of introduction against the firm’s rational expectation of the lifetime profitability of the product based on static observ- 59_{Levitt(1965) famously said, “The concept of the product life cycle is today at about the stage that the}

Copernican view of the universe was 300 years ago: a lot of people knew about it, but hardly anybody seemed to use it in any effective or productive way.”

60_{Chambers, Mullick and Smith(1971) discuss various forecasting methods for the product life cycle;Sam-} pere(2014) mentions Xiaomi’s product strategy around the length of its product life cycle.

able product and market characteristics. Specifically, I let firms approximate the expected lifetime profits of a new product, by relating its lifetime profits to its short-run profits at release,

EP_jm(J_mtjm

0 ) =E(xjmtjm₀ ,wjmtjm₀ )pjmt0jm(Jmt0jm)·PLCdjm, (1.3.7)

where firms first form beliefs about the magnitude of the product life cycle, based on char-

acteristics of the product and the market at launch-time, for product j, released att₀jm in

provincem,

d

PLCjm= qPLCX_jmtjm

0 , (1.3.8)

where the parameters qPLC is what firms use to make their best linear predictions, and

remain to be estimated.

The dynamic product portfolio game specified in equation (1.3.6) can be then reformu-

lated as follows: Firms simultaneously choose a set of non-flagship products (given their flagship products exogenously) to maximize their own expected profits, given the other

firms’ portfolios, or the market product configurationJ,

P_{f mt}= max Jf mt✓Jf,t_{j2Jf mt}

Â

_{,j2Jf m,t 1} [E(xjmt,wjmt)pjmt(Jmt) Fjmt] +

Â

l2Jf mt,l62Jf m,t 1 [E(xlmt,wlmt)plmt(Jmt)·PLCdlm SClmt], (1.3.9)

where the expected static profits are integrated over Stage II shocks, and lifetime profits are approximated with firms’ rational beliefs about product life cycles—both of which are

determined by the market product configuration J, as a result of firms’ portfolio competi-

tion62_.

Necessary equilibrium conditions of this game then require every firm f to consider

all possible subsets of the potential-product pool J_f,t (or the power set) in each market-

62_{This game specified in equation (1.3.9) also assumes no economies of scope for either introducing a new}

product, or maintaining an existing one. This is fairly standard in the literature. Empirically, product entries plausibly do not exhibit economies of scope, given the setup of large manufacturers’ regional offices and low transportation costs of smartphones. I also do not model the actual development of products, but only their introductions to the market, after they are developed. Product maintenance could potentially exhibit economies of scope. I argue that, with small product configuration changes in the counterfactual, this effect is likely small.

month(mt), and have no incentive to deviate from the chosen product portfolioJf mt. These conditions are fairly weak and typically yield many equilibria in positioning games such

as equation (1.3.9). In the estimation to follow, I only build off these necessary conditions to

make inference on sunk and maintenance cost parameters. In the counterfactual analysis, I rely on firms’ best-response dynamics to select equilibrium.

Finally, sunk costsSCjmt =SC(qSC,Xf m|µjmt)also vary with the smartphone manufac-

turer, and which market the product is introduced into, with ani.i.d. shockµjmt observed

by firms at the beginning of Stage I. Maintenance costsFjmt = F(qF,Xjm|hjmt)are shifted

by observable characteristics of the product, the type of retail channels, and the market,

with ani.i.d. shockhjmtalso observed by firms at the beginning of Stage I.

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