2. In a market equilibrium, the marginal rate of substitution between goods A and B equals the price ratio of goods A and B. That is, $\frac{U_A}{U_B} = \frac{p_A}{p_B}$, where $U$ is the utility function.
a. Derive the equilibrium condition if utility is not $U$ but $\alpha + \beta U$.
b. What does this imply about what we know about total utility and hence total value?