“Better an egg today than a hen tomorrow” on the implications of deaccess policies for donations to museums

Abstract

Severe budget cuts in the cultural sectors of many countries have spurred disparate suggestions for alternative sources available to public institutions. Deaccessioning may be an option, although controversial, to guarantee the survival of cultural institutions. This paper addresses the consequences that deaccessioning may have on donations of artworks to museums, by developing a sequential game with incomplete information. We investigate the interactions between donors and museums, when the former is uncertain about the commitment of a museum not to deaccess part of its endowment in the future. Our analysis shows that deaccessioning may reduce art donations to museums. Interestingly, public grants to museums cause a negative externality to a committed museum, which experiences a reduction in donations. Results provide intuitions for the widespread resistance to deaccessioning of museum associations, for their efforts to enforce common regulation restricting the use of proceeds to the acquisition of art, and also for the proliferation of private art museums.

Appendices

Appendix

Comparative statics

• Donations are lower when the signal is $\rho _{1}<1$, i.e. $g(\rho _{1}<1) < g(\rho _{1}\ge 1)$:

  $$\begin{aligned} \begin{array}{c} g(\rho _{1}<1) = w - \frac{\alpha + \beta }{ a \alpha } < w - \frac{\alpha + \beta }{ a }\left( \frac{p}{p + q(1-p)}\beta + \alpha \right) ^{-1} = g(\rho _{1}\ge 1) \\ \frac{p}{p + q(1-p)}\beta + \alpha > \alpha \end{array} \end{aligned}$$

  (12)

• Donations are increasing in a and w:

  $$\begin{aligned} \begin{array}{ccc} \frac{\partial g(\cdot )}{\partial w} = 1 >0;&\frac{\partial g(\rho _{1}< 1)}{\partial a} = \frac{\alpha +\beta }{a^{2}\alpha } >0;&\frac{\partial g(\rho _{1}\ge 1)}{\partial a} = \frac{\alpha +\beta }{a^{2}\left( \mu \beta +\alpha \right) } >0; \end{array} \end{aligned}$$

  (13)

• Donations after the signal $\rho _{1}< 1$ are:

  • increasing in $\alpha$:

    $$\begin{aligned} \frac{\partial g(\rho _{1}< 1)}{\partial \alpha } = \frac{\beta }{a \alpha ^{2}} > 0; \end{aligned}$$

    (14)

  • decreasing in $\beta$:

    $$\begin{aligned} \frac{\partial g(\rho _{1}< 1)}{\partial \beta } = -\frac{1}{a \alpha } < 0; \end{aligned}$$

    (15)

• Donations after the signal $\rho _{1}\ge 1$ are:

  • increasing in $\mu$:

    $$\begin{aligned} \frac{\partial g(\rho _{1}\ge 1)}{\partial \mu } = \frac{\partial }{\partial \mu } \left( w - \frac{1}{\mu a + (1 - \mu )a\rho _{2}^{*}} \right) = \frac{(1 - \rho _{2}^{*}) a}{\left( \mu a + (1 - \mu )a\rho _{2}^{*}\right) ^{2}} > 0; \end{aligned}$$

    (16)

  • increasing in the probability p, since $\mu = p/p + q^{e}(1-p)$ and:

    $$\begin{aligned} \frac{\partial \mu }{\partial p} = \frac{q^{e}}{(p + q^{e}(1-p))^{2}} > 0; \end{aligned}$$

    (17)

  • decreasing in $q^{e}$, since:

    $$\begin{aligned} \frac{\partial \mu }{\partial q^{e}} = -\frac{p(1-p)}{(p + q^{e}(1-p))^{2}} < 0; \end{aligned}$$

    (18)

  • decreasing in $\beta$:

    $$\begin{aligned} \frac{\partial g(\rho _{1}\ge 1)}{\partial \beta } = \frac{\partial }{\partial \beta } \left( w - \frac{\alpha +\beta }{a}\frac{1}{\mu \beta + a} \right) = - \frac{(1 - \mu ) \alpha }{a \left( \mu \beta + \alpha \right) ^{2}} < 0; \end{aligned}$$

    (19)

  • increasing in $\alpha$:

    $$\begin{aligned} \frac{\partial g(\rho _{1}\ge 1)}{\partial \alpha } = \frac{\partial }{\partial \alpha } \left( w - \frac{\alpha +\beta }{a}\frac{1}{\mu \beta + a} \right) = \frac{(1 - \mu ) \beta }{a \left( \mu \beta + \alpha \right) ^{2}} > 0; \end{aligned}$$

    (20)

• Furthermore, we have that (note that $q^{e}>0$ implies $\mu >0$):

  $$\begin{aligned} \begin{array}{c} g(\rho _{1} \ge 1 | q = 0) = w - \frac{1}{a} > w - \frac{\alpha +\beta }{a} \left( \mu \beta +\alpha \right) ^{-1} = g(\rho _{1}\ge 1| q^{e} > 0) \\ \frac{\alpha +\beta }{\mu \beta +\alpha } > 1 \iff (1-\mu )\beta > 0; \end{array} \end{aligned}$$

  (21)

• Perfect Information Benchmark:

  $$\begin{aligned} \begin{array}{c} g(co) = w - \frac{1}{a} = g(\rho _{1}\ge 1| q^{e} = 0); \\ g(nco) = w - \frac{\alpha + \beta }{a\alpha } < w - \frac{\alpha + \beta }{a(\mu \beta + \alpha )} = g(\rho _{1}\ge 1| q^{e} > 0); \end{array} \end{aligned}$$

  (22)