= Solution
The reservation bid price for a claim $Y$ is the fixed cash payment $p_i(Y)$ which leaves the agent indifferent: $E[U_i(X_i+Y-p_i(Y))]=E[U_i(X_i)]$. For Gaussian wealth $W$, <exponential utility> is $-\exp[-\gamma_iE(W)+\gamma_i^2\operatorname{Var}(W)/2]$, so its <certainty equivalent> is $E(W)-\gamma_i\operatorname{Var}(W)/2$. For $Y=\lambda X_0$, subtracting the original <certainty equivalent> gives
$$
\boxed{p_i(\lambda)=-\tfrac12\gamma_i(\lambda^2v_{00}+2\lambda v_{0i}),\qquad\lim_{\lambda\to0}\frac{p_i(\lambda)}\lambda=-\gamma_i v_{0i}.}
$$
The marginal price is positive when the claim hedges the agent's endowment, negative when it adds positively correlated risk, and zero for an uncorrelated zero-mean infinitesimal position.
Assume $v_{00}>0$, so the claim is nontrivial. Buying $\theta$ units at per-unit price $p$ changes the <certainty equivalent> by $-(p+\gamma_iv_{0i})\theta-\gamma_iv_{00}\theta^2/2$. This strictly concave quadratic is maximized at $\theta_i=-(p+\gamma_iv_{0i})/(\gamma_iv_{00})$. Market clearing $\sum_i\theta_i=0$ gives
$$
\boxed{p=-\Gamma\sum_i v_{0i},\qquad\Gamma^{-1}=\sum_i\gamma_i^{-1},\qquad\theta_i=\frac{\Gamma v_{0\bullet}-\gamma_iv_{0i}}{\gamma_iv_{00}}.}
$$
At the optimum the certainty-equivalent gain is
$$
\boxed{\Delta_i=\frac{(\gamma_i v_{0i}-\Gamma v_{0\bullet})^2}{2\gamma_i v_{00}}.}
$$
The maximal expected utility equals the original negative utility multiplied by $e^{-\gamma_i\Delta_i}$, hence is improved. Paying a fixed amount $\Delta_i$ removes exactly that gain, proving it is the fixed-payment value of market access. If $v_{00}=0$, the Gaussian claim vanishes almost surely, all its <covariances> vanish, and the appropriate price and access value are zero; the printed formulas with a <variance> denominator require the nontrivial-claim assumption.
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