I am trying to interpret the marginal rate of substitution stidied in an article. The article in question is Burbidge, J. B., Robb, A. L., 1980. Pensions and retirement behaviour. The Canadian Journal of Economics 13 (3), 421–437. https://www.jstor.org/stable/134702?seq=1. I paste a screenshot of the equation in question. $U^{'}$ is utility from retirement. $U^{o}$ is utility from full-time work. $Y$ is labor income. $R$ is retirement age. $P$ is pension income. $T$ is how many years the agent lives. $r$ is the discount rate. The left-hand side of this equation is the discounted ratio of the marginal utility of another year of retirement to the marginal utility of an increase in consumption per year, that is, the marginal rate of substitution (MRS). I question when this MRS is larger. I consider the right-hand side of the equation, and in particular the term $Y(R)-P(R,\alpha)$. The first component of this term is work income if one was to work full-time at age $R$. The second component is the pension income if one was to retire at age R. Assuming that $\theta = 0$, the term represents the difference between full-time work income and pension income at age $R$. Suppose the term is positive. This means that income from work is larger than income from retirement if one decided to work instead of to retire at age $R$. Suppose that we increase the magnitude of this term. Then working pays more than retirement does. This makes the right-hand side larger. Then, the left-hand side must be larger. A larger left-hand side means that the marginal utility from retirement, relative to the marginal utility from consumption, is higher. But this looks odd. If working pays more (right-hand side), why would the agent derive more utility from retirement (left-hand side)?

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