# Introduction As a business leader, investor, engineer, or policymaker, you don’t only need to assess how much to invest in one particular technology. You also need to think more broadly about the full range of technologies you’re going to choose to invest in, and how you’ll spread your resources between them. The challenge in investment, of course, is that the future is inherently uncertain. The classic financial approach to handling uncertainty is diversification: investing in a range of assets so that if one underperforms, you won’t lose everything. However, in the context of technology, this strategy runs up against the phenomenon captured by Wright’s Law. Namely, if your investment is large enough to meaningfully affect effort levels, the technology will improve because of your investment. In some cases, technology improves rapidly with effort, so investing in a single technology will bring far greater rewards. How, then, can an investor both protect against risk and capitalize on the benefits of focused investment? The solution lies in finding the right balance between diversifying investments across different technologies and concentrating on the most promising ones. Identifying the right level of diversification is the key to arriving at a successful technology portfolio. The right level of diversification will depend on the forecasts of improvement for the set of technologies under consideration and the uncertainty associated with those forecasts. So in this section, we’ll consider technology portfolios. We’ll construct a single analysis framework that can help decision-makers achieve the outcomes they seek from their investments in technology. # Technology portfolio problem Though you may never have heard the term “technology portfolio optimization problem” before, you’ve encountered it in many contexts. A technology portfolio is simply an investment of financial resources or time in one or more technologies. Decision makers face technology portfolio optimization problems whenever they have to decide how they’re going to allocate their resources across different technologies. Here are several examples of different decision-makers and the types of technology portfolio problems they face: - Technology firms: Companies that develop and market technologies usually need to choose which different technologies or technology designs to focus their R&D budgets on. They may also need to decide how to allocate levels of production across different technology product lines. A technology start-up, for example, must decide how to best invest across different technology designs when pursuing R&D, pursuing a demonstration project, and scaling up production. A mature firm needs to stay ahead of competitors by developing new products or continuously improving existing ones. In all these contexts, firms must decide how much to concentrate or diversify their investments in R&D and production across different technologies to support innovation. The objective of these portfolios is usually to maximize the improvement in the cost per unit service, either by reducing the cost for the same technology-based service or by improving the technology-based service. - Investment firms: Investment firms focused on technology companies or industries that depend on technology innovation to succeed also must address technology portfolio problems. Some firms may invest directly in the production or installation of technologies. Others will invest in companies that are working to gain or maintain market share. In all these cases, it is essential to find the right level of diversification versus concentration of their investment portfolios. To find that balance, it will be important to forecast both rates of technological innovation and the uncertainty around those trends, and to then use those forecasts to optimize portfolios. The objective in these cases may be purely profit-oriented or focused on profit plus other measures of performance. But in either case, the optimal solution will balance anticipated rates of improvement and associated uncertainties. - Policymakers investing in market-based incentives: Government officials also face technology portfolio problems when developing policies designed to expand markets for particular technologies or to more generally direct markets toward the public good. They also face technology portfolio problems when directing funds for government research and development. Consider, for example, a policymaker deciding on technology regulations. The choice of regulation will affect the portfolio of technologies that emerge in the marketplace, offering different capabilities or services. If, for example, regulations are enacted to prevent emerging large language models such as ChatGPT from presenting information on individuals, that will change the array of these artificial-intelligence-informed technologies that are offered to the public. Or if policymakers increase the stringency of regulations limiting vehicle tailpipe emissions, the portfolio of vehicles will shift in the direction of low emissions. Policymakers can direct markets in other ways as well, including through subsidies for certain technologies, guaranteed prices for a given technology-based service, or market-based interventions that allow companies to purchase and trade credits for externalities, such as greenhouse gas emissions. In any of these situations, deciding how to intervene in the market can be viewed as choosing which technology portfolio will best serve the public; a technology portfolio problem. Policymakers thus need to both predict the portfolios that will result from proposed policies (i.e. the portfolio that the market will solve for under a set of conditions) and to assess which portfolio best serves the public interest. The approach described in this section provides a principled way of approaching these analyses, which will support better decisions. - Policymakers investing in public infrastructure and services: The government also buys technology directly. Public utilities, other physical infrastructure, and public services all require technology investments. So policymakers directing these purchasing decisions also face technology portfolio problems. These decisions can be weighty and difficult to change: A single large investment, such as in a particular public health program, can have long-term consequences. Diversification can help protect against negative outcomes for any substantial direct investment. - Government research and development investments: Government decision-makers funding R&D must also solve technology portfolio problems. Policymakers allocate budgets across agencies for health, defense, energy, agriculture, etc. Government agencies must then decide how to allocate R&D funding across programs, or how to fund projects within a program. Since R&D is designed to increase effort into technological development, forecasting must use models that depend on effort levels rather than time. To forecast how technology may respond to R&D, decision-makers can consider specific ‘low-level’ improvement mechanisms and types of effort for investment, using mechanistic models like the one we covered earlier in the course. The control variables in these portfolios are the amount of funding allocated across agencies, programs within agencies, and projects within programs. The objectives for government-funded research often focus on externalities, for example by reducing the cost per unit service of a technology that addresses an environment- or health-related problem. - Technology researchers in the private sector, at universities, or in government labs: Teams of scientists and engineers working in a variety of contexts—and even individual researchers—must decide how much time and economic resources to allocate to different research ideas and projects. Research team managers may assign team members to a diversified set of technology research projects because of the uncertainty around whether any given one will succeed. In this example, the control variables would be the team members’ time, though managers may also diversify their investments of economic resources in the equipment and infrastructure needed to support the different projects as well. The objectives can vary: Government-funded research may address externalities. Private R&D often focuses on cost per unit service (as reflected in the market price), but may also address externalities that consumers value. Individual researchers, working in private companies, government labs, or universities, may have deadlines by which they need to demonstrate a result. In this case, they may solve a portfolio problem, allocating their time across different technology designs or experimental protocols, to increase their chances of delivering a result by the deadline. # Elements of a technology portfolio There are five elements needed to define a technology portfolio. ## Decision makers There are three main categories of decision-makers who are faced with technology portfolio problems: **private investors** (e.g., firms), **government actors** (e.g., policymakers), and **engineers**. The portfolio model is set up to allow these decision-makers to decide how to invest across technologies to meet their goals. ## Objectives The objectives of the portfolio reflect the decision-maker’s goals. For example, leaders of companies may want to maximize the market competitiveness of their products. This is generally reflected in the metric of cost per unit service, and improvement is achieved either by bringing down the cost or by improving the service. Policymakers typically want to address externalities not captured in the market price, such as health impacts or environmental degradation. They may do so by choosing an objective, such as pollution per unit service or water intensity per unit service. They may also do so by minimizing the cost per unit service while imposing a constraint (see below) that reflects the externality. ## Control variables Control variables (also known as decision variables) are the quantities that decision-makers control and can make decisions about. The control variables may represent monetary investments in technology development firms, technology production, R&D, or demonstration, or they may represent the time invested in research and development. ## Technology attributes Technology attributes reflect the performance of the technologies being considered. They are measured by performance intensity metrics, such as cost per unit service, greenhouse gas emissions per unit service, or water usage per unit service, based on the decision maker’s objective. These technology attributes can, of course, change substantially with innovation, and modeling this change is a key part of creating a technology portfolio model. If the time horizon of interest for the decision maker is very short or the technologies do not have much innovation potential, we model these attributes as static. Otherwise, we model them as changing with time (following Moore’s Law) or with effort (following Wright’s Law). ## Constraints Constraints are the limitations on the set of possible solutions to a portfolio problem and can come in many different forms. Production capacity may be limited: Raw materials availability may set limits on the total production achievable. These limits would be reflected in the assessment of the scalability of the technologies (i.e., in the scalability metrics covered earlier in the course), as defined by the total availability of a mined material, for example. The rate of production growth may also be limited. Factories, for example, may only be able to manufacture a given number of units of a technology per year. That capacity may be able to grow with investment, but the rate of that growth may be limited. These constraints on the year-to-year changes in the portfolio do not only arise on the manufacturer’s side. They can also come from the consumer’s side. If you invest in Technology A and decide to switch to Technology B, it may require an investment of time and economic resources to make that change possible, such as by changing software to meet hardware requirements. The switching cost may effectively limit the year-to-year change that is practicable. Sometimes it is essential that the demand for the technology service is met, such as vaccine production being sufficient to serve a population. Regulations may specify levels of performance of the portfolio along a particular dimension, such as by limiting greenhouse gas or tailpipe emissions. In addition, a baseline constraint when developing a technology portfolio model is that levels of technology production or investment are non-negative since that would make no sense. Addressing a portfolio problem means finding an investment scenario that meets the decision-makers' objectives while remaining within the specified constraints. # How externalities are reflected in technology portfolio optimization problems Because the role of government is to support the well-being of their constituents, the objectives of policymakers typically include a consideration of externalities that are not captured in the market price. In fact, addressing externalities is why policy is needed in the first place. So, in conceptualizing the choice of government policies as a technology portfolio problem, how do we include a consideration of externalities? There are two approaches policymakers can take to this. The first is to focus on the externality as the quantity to be minimized. In other words, the externality is central to the objective. For example, the policymaker may be interested in minimizing environmental impact per unit service, such as greenhouse gas emissions per kilowatt-hour. The second approach would be for the policymaker to impose constraints to reflect the externality while choosing the objective of minimizing the cost per unit service. For example, the policymaker might impose the constraint of limiting economy-wide greenhouse gas emissions to a specific number. Another possible constraint might be a demand constraint, such as providing subsidies for vaccine production to serve the demand of the entire population. # The objective function Imagine you have an objective for your technology portfolio, and you have the decision variables that you can control. How then do you solve for the optimal values for your control variables (i.e. the optimal decision) to meet a particular objective over a period of a given number of years? Here we’ll show how to calculate that. For simplicity, we’ll assume that your objective is minimizing cost per unit service and that your portfolio contains just two technologies. The idea is that for each year $t$, you simply add up the costs of each technology in your portfolio (which is the per-unit cost of each technology multiplied by the quantity for that year, so $c_ix_{it}$). Since you’ll be doing this over time, you’ll want to include a discount factor for costs from future years; future gains or losses are less impactful than immediate ones. So in year $t$, you’ll multiply the sum of that year’s costs by $(\large \frac{1}{1+r})^t$, the standard method of discounting. The goal, then, is to choose the quantities of each technology in each year (that is, all the $x_{it}$​) to minimize this equation: $\large C_0 = \sum_{t=1}^{T} \delta^t \left[ c_1 x_{1t} + c_2 x_{2t} \right]$ Subject to: $x_{1t} + x_{2t} = d_t, \quad \text{for all } t$ $x_{1t} \geq 0, \quad x_{2t} \geq 0 \quad \text{for all } t$ Where: $d_t = \text{demand in year }$ $T = \text{decision horizon}$ $\delta = \frac{1}{1 + r} = \text{discount factor}$ The portfolio solutions must satisfy two constraints in this example: that a specified level of demand must be met, and that the values for the control variables (the technology investments) can’t be negative. In this example, the costs per unit service of the two technologies ($c_1$ and $c_2$) are treated as static. This could be the case for technologies that are very close to their raw material forms and therefore close to their cost floors. Often, though, those costs will change over time and with production. To account for this, $c_1$ and $c_2$ can be expressed as functions of time or of production. They can be modeled using Moore’s Law or Wright’s Law plus uncertainty estimates. # How innovation forecasts can inform technology portfolio decisions Here we’ll review two examples of technology portfolio optimization problems, and we’ll consider the situations under which it will be optimal to concentrate or diversify the portfolio. We will pay special attention to how technology innovation forecasts will factor into those decisions when solving the portfolio problem. Suppose you’re an administrator of a large educational organization that serves students internationally through remote learning. You’re responsible for choosing digital devices with internet connectivity to distribute to the students, who typically lack access to these technologies at home. You have a choice between desktop computers, laptops, and tablets. You are facing a technology portfolio problem: Which devices should you invest in? The elements of this portfolio problem are displayed in the table below: | Decision maker | Educational organization | | --------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | Objective | Minimize the cost per unit service of supplying remote study capability | | Control variables | Investment allocation between digital devices | | Constraints | Functionality standard: a minimum level of service quality must be provided<br><br>Demand constraint: demand for devices must be met<br><br>Technology acquisition constraint: there is a limited number of each device available for purchase | | Technology attributes | Cost per unit service | First, we’ll assume you need to decide only for the next year or two, and that all three technologies are plenty functional for the students’ needs (i.e., they each meet the minimum service quality constraint). If the supply of all three devices is sufficient to meet your needs — in other words, the technology acquisition constraint is met — the choice is clear: you’ll just buy whichever is cheapest, say tablets, with no diversification required. But suppose there aren’t enough tablets available for purchase for all your students. Then you’ll need to diversify your portfolio to meet the demand constraint by purchasing some laptops (the next cheapest, i.e., the second performing technology in cost per unit service) in addition. The solution would be to purchase as many tablets as possible, up to the technology acquisition constraint, and then purchase laptops to meet the demand constraint. To take a slightly more complex case, now let’s suppose you have to make a purchasing decision not just for next year but for the next five years, in order to ensure that you will receive a sufficient number of devices to serve your population of students. This might be the case if, for example, you are a large educational organization and you need complete certainty that you will be able to deliver devices to each learner. Given how quickly digital devices have been evolving and how much they can still evolve and improve, how would the solution change? Let’s restrict the decision in this case to tablets and consider how you would decide which type of tablet to purchase. To answer that, you’ll need to forecast the cost per unit service for the various devices over a five-year period. You can do this either using Moore’s Law or Wright’s Law. In most situations, your organization’s purchases won’t be large enough to make a significant difference in cumulative production, since these devices are used for many different applications, and you represent only a small fraction of those overall sales. In that scenario, you’ll want to use a time-based forecast, such as Moore’s Law. But in some scenarios, your purchases might be large enough to affect the overall market for a device, significantly impacting cumulative production. For example, suppose your students often live in very remote locations with limited electricity and bad-quality internet. Say you are a relatively large organization, and you are considering purchasing a particular type of tablet being developed by a smaller-scale manufacturer. The reason you are considering those tablets is that the manufacturer is focusing on developing devices that use small amounts of power and include signal boosters. These devices may be especially useful for the students you are serving, particularly where internet and electricity services are more limited. In such a situation, if your decision will measurably affect the overall production level of the manufacturer, you’ll need an effort-based model like Wright’s Law to forecast how technology attributes such as cost per unit service are likely to change in response to investment. In either case, you might start by assuming there’s no uncertainty in how quickly the technologies will improve (i.e., there’s no uncertainty in the parameters for Moore’s Law or Wright’s Law), for simplicity’s sake. Then you can forecast the cost of each technology in each year, in the case of Moore’s Law, or with each additional unit produced, in the case of Wright’s Law. You would then choose the device with the lowest cost per unit service each year in the case of Moore’s Law. Or, if applying Wright’s Law, you would choose the device that gives you the least cost per unit service overall when considering the cumulative production over the five-year period. These solutions would, of course, have to fall within the specified constraints. If you think there’s significant uncertainty in the rates of improvements, though, you’d be better off diversifying your purchases to protect yourself from possible scenarios in which the technology that is forecasted to offer the best cost per unit service turns out to offer poorer service than an alternative. Another situation in which you might be wise to diversify is when there's a switching cost, even if you aren't obliged to commit years in advance. For example, you might have to format lessons differently to work with different displays, software, and device speeds. If making those changes quickly would be impractical, you may be better off diversifying some from the beginning so that the development can be done more methodically at lower cost.