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Substituting in our last result we have:
:<math>-\mathbb{E}\left[ e^{-r\left[ c_{1}+b_{1}(\eta +a_{1}+\varepsilon_{1})-g(a_{1})+\beta \left( (1-b_{2}^{*})\left[ \frac{h_{1}}{h_{1}+h_{\varepsilon }}\cdot m_{1}+\frac{h_{\varepsilon }}{h_{1}+h_{\varepsilon}}\cdot (\eta +a_{1}+\varepsilon_varepsilon _{1}-a_{1}^{*})\right]+b_{2}^{*}(\eta +a_{2}^{*}(b_{2}^{*})+\varepsilon_{2})-g(a_{2}^{*}(b_{2}^{*}))\right) \right] }\right\],</math>
Which can be written in certainty equivalent form as:
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