# COVID-19 and the value of safe transportation in the United States

The possibility of transmission of COVID-19 introduces an additional margin in the choice of means of transport for commuters. Modeling of transport economics can be used to highlight this choice. We will define the notion of pass-through-avoid-value (VAT), which captures the trade-off between a higher dollar or time cost of transportation and a lower likelihood of disease transmission, possibly due to exposure to a smaller number of travelers, resulting in a likelihood of weaker infection. A central concept of transport economics is the travel time value (VOT), which quantifies the well-known trade-off between saving time and money. More precisely, YOUR specifies the amount of money that if a commuter had the choice between paying this amount and benefiting from a fixed time saving during his journey, or paying nothing and receiving no time saving, he would be exactly indifferent between the two options . The similar notion of statistical life value (VV) is used in actuarial studies to quantify the trade-off between the reduction in the probability of death and a corresponding reduction in income that makes the agent indifferent.7.8. YOUR is of paramount importance in the modeling of transport demand, as well as in the cost-benefit analysis of related public policies. For example, travel time and reliability have been found to account for 45% of the average social variable cost of travel in the United States.9.

In the era of COVID-19, there is an additional cost associated with public transportation, namely an increased likelihood of exposure to the virus, resulting in potential illness and associated economic costs. When it comes to commuting, these costs can be modeled parallel to the costs of potential traffic accidents. Exposure to the virus, just like a traffic accident, occurs with some probability on every trip. Also, just as the likelihood of an accident increases with congestion, the likelihood of infection increases with the number of people using the mode of transportation under study. The VAT can be used to monetize the desire to reduce the likelihood of infection by appropriately adjusting the choice of mode of transport.

Transportation studies have explored the relationship between YOUR and income, wealth, age, time constraints, etc. Modeling of travel demand generally reveals that travel time is an important explanatory variable, even more so than the direct economic cost of travel. The standard model is based on Lavaten, while more involved theories of YOUR rely on the optimal time allocation framework11. People in this framework choose the amount of work to be done since the total time spent on work, leisure and travel equals the total time they have available. Since time can be transferred between work and play, any marginal savings in travel time can be used to increase labor income. Intuitively, optimization implies that travel time is valued at the after-tax wage rate. The commuter budget constraint can be expressed as

$$x + c le left ({1 – tau} right) w cdot h$$

(1)

while the commuter’s time constraint gives

or T is the total time available, t is the time spent traveling, h are hours spent at work for after-tax income, (Y = left ({1 – tau} right) w ), and (the) refers to time spent on leisure. Ultimately, X is the expenditure on goods, and vs is the direct cost of transportation. If the worker uses public transport, vs would be the public transport fare; if the worker uses private transport, vs would be the cost of fuel needed for the trip; that is, the price per gallon multiplied by the miles driven divided by the miles per gallon (or ({{fuel ; price times miles ; driving} mathord { left / { vphantom {{fuel ; price times miles ; driving} {, fuel ; efficiency}}} right. kern- nulldelimiterspace} {, fuel ; efficiency}} )). Rental V denotes the optimal value of the utility function, you, the first order conditions for this problem give

$$VOT = frac {{{ raise0.7ex hbox { { partial V} } ! Mathord { left / { vphantom {{ partial V} { partial t}}} right . kern- nulldelimiterspace} ! lower0.7ex hbox { { partial t} }}}} {{{ raise0.7ex hbox { { partial V} } ! mathord { left / { vphantom {{ partial V} { partial h}}} right. kern- nulldelimiterspace} ! lower0.7ex hbox { { partial h} }}}} = left ({1 – tau} right) w + frac {{{ raise0.7ex hbox { { partial u} } ! mathord { left / { vphantom {{ partial u} { partial h}}} right. kern- nulldelimiterspace} ! lower0.7ex hbox { { partial h} }} – { raise0.7ex hbox { { partial u}  } ! mathord { left / { vphantom {{ partial u} { partial t}}} right. kern- nulldelimiterspace} ! lower0.7ex hbox { { partial t}  }}}} { lambda}$$

(3)

or ( lambda ) is the marginal utility of money. The YOUR increases with the after-tax wage rate and decreases with the marginal utility of money. This leads to self-selection where commuters with a higher opportunity cost will tend to choose faster and generally more expensive modes of transport.

Recent events related to COVID-19 highlight additional constraints and concerns related to public transport. As shown in Figs. 2, 3, 4 and 5 later in the “Data visualization” section, there is evidence that the density of public transport options is strongly correlated with an increased likelihood of virus transmission.3,4,5,6. This introduces an additional compromise. The increased use of public transport could lead to a higher likelihood of loss of income due to infection and subsequent illness.

Consider a commuter during the COVID-19 era. Whenever he uses public transport, there is a probability, (P left (n right) ), to contract the virus. This probability increases in number of passengers, m, since contact between commuters, direct or indirect, with other passengers increases the likelihood of contact with a COVID-19 carrier. Travel time, (t left (n right) ), also increases with m, since higher capacity utilization implies longer delays. The expected utility for a commuter is given by

$$U = P left (n right) cdot u ^ {V} left ({Y – F – L} right) + left[ {1 – Pleft( n right)} right] cdot u ^ {- V} left ({Y – F} right) – C left ({t left (n right)} right).$$

(4)

In the above expression, Yes is the commuter’s income, while (u ^ {V} ) and (u ^ {- V} ) represent the resulting utilities if the commuter is infected and uninfected, respectively, during the commute to work. Infection can lead to medical costs and loss of income due to sick leave due to mild or severe symptoms, and in extreme cases even death. We denote the resulting expected loss of income by THE, and the price of the trip as F. Ultimately, (C left ({t left (n right)} right) ) denotes the opportunity costs of commuting time, where ({{ partial C} mathord { left / { vphantom {{ partial C} { partial t}}} right. kern- nulldelimiterspace} { partial t}}> 0 ). Thus, increasing travel time increases travel costs.

The likelihood of disease transmission will vary with different modes of transport. For example, this probability should be close to zero if you go to work with your own car, especially if it is not a carpool. The likelihood will increase when using carpooling services or traditional taxis because, although the driver may be the only other person in the vehicle, disease contagion from previous passengers is still possible. In a bus or a train, the probability increases with the number of traveling companions, m.

The model illustrates how infection risk and travel time relate to commuting density as captured by the number of people, m, using this particular means of transport. The marginal change from an increase in the number of commuters can be decomposed into an increase in (a) the implicit risk of infection, and (b) the travel time. The expected marginal utility of income is defined as8:

$$lambda = P cdot frac {{ partial u ^ {V}}} { partial Y} + left[ {1 – P} right] cdot frac {{ partial u ^ {- V}}} { partial Y}.$$

(5)

To avoid an exogenous increase in travel time, commuters would be willing to pay ( frac {1} { lambda} frac { partial C} {{ partial t}} ). This is the standard expression of the YOUR discussed earlier. The value of an exogenous increase in the risk of transmission of infection is (- frac {1} { lambda} left ({u ^ {V} – u ^ {- V}} right) ). The value of choosing a mode of transport that involves a marginal reduction in the number of people commuting, thus resulting in a lower probability of infection, is given by

$$frac {1} { lambda} left[ {left( {u^{V} – u^{ – V} } right) cdot frac{partial P}{{partial n}} + frac{partial C}{{partial t}} cdot frac{partial t}{{partial n}}} right].$$

(6)

In this context, we will refer to ( frac {1} { lambda} left ({u ^ {V} – u ^ {- V}} right) cdot frac { partial P} {{ partial n}} ) as the pass-through-avoid-value (VAT). Equation (6) captures the combined value of reduced risk and reduced travel time that would be afforded by a small reduction in the number of people commuting. This could be, for example, the result of using a different (or less congested) mode of transport. Equation (6) can provide an interpretation of our empirical work related to the marginal rate of substitution between modes of transport associated with different probabilities of infection.