Is the Price System or Rationing More Effective in Getting a Mask to Those Who Need It Most?
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Is the Price System or Rationing More Effective in Getting a Mask to Those Who Need It Most? Alistair Munro1 Accepted: 13 July 2020 / Published online: 4 August 2020 © Springer Nature B.V. 2020
Abstract Weitzman’s classic insight on the virtues of allocating a scarce good via the price system or through rationing is applied to the problem of distributing masks, when the use of a mask provides a positive external benefit. I show that if a market leaves some individuals without a mask (when potentially there is supply for all), then rationing may be the superior option. When the variation in need is small, then even if the external effect of mask wearing is approximately equal to the personal benefit, even 10–20% maskless in the population may justify rationing. Keywords Weitzman · Covid-19 · Masks · Prices versus quantities
1 Introduction In many countries masks have been recommended as a means of reducing the risks of being infected with the Covid-19 virus (WHO 2020). But masks, especially those of reasonable surgical quality, are in short supply. How then should they be allocated? South Korea is one of a number of countries that have used rationing to control access to face masks during the Covid-19 pandemic (Kim 2020) [see also Taiwan, Everington (2020)], while other countries have relied on the market to allocate masks outside the hospital sector. In this paper, I apply methods from the late Martin Weitzman’s famous articles on rationing, Weitzman (1974) and Weitzman (1977) to examine the issue.
2 Theory To fix ideas, I suppose the good to be a mask of reasonable quality, in the sense of providing some protection against infection in everyday use without necessarily meeting standards expected for medical workers. A higher amount of x means that a person consumes each mask for a shorter period before disposal. * Alistair Munro alistair‑[email protected] 1
National Graduate Institute for Policy Studies (GRIPS), Roppongi 7‑22‑1, Minato‑ku, Tokyo 106‑8677, Japan
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Following the notation of Weitzman (1977), let the utility function of an individual be,
u(x) =
(A + 𝜖)x x2 − − 𝜆px B 2B
(1)
where x is the amount consumed, p is the price per unit, A, and B are parameters1 (with B and A positive), while 𝜆 represents the inverse of the marginal utility of income and 𝜖 is a taste or need parameter for x. The idea behind Eq. 1 is that it represents a second order approximation to a more general utility function. Need may vary because, for example, risk aversion varies or intolerance to wearing a mask varies, but also because the likely consequences of infection are heterogeneous (Jordan et al. 2020). As in the original Weitzman (1977) model, the normalizations of E(𝜖) = 0 and E(𝜆) = 1 are employed, where E(.) represents the mean over the n members of the society and where it is assumed for simplicity that 𝜖, 𝜆 are distributed independently. For a consumer in this situation faced with an unrestricted market, the demand for x is given by, x(𝜖, 𝜆) = A − B𝜆p + 𝜖 Weitzman compares
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