ENADE Ciências Econômicas Practice Questions - ENADE Ciências Econômicas - Exame Nacional De Desempenho Dos Estudantes Exam

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A consumer has the Cobb-Douglas utility function $U(x_1, x_2) = x_1^\alpha x_2^\beta$, where $\alpha > 0$, $\beta > 0$, and faces prices $p_1 > 0$, $p_2 > 0$, and income $I > 0$. What is the fraction of total income allocated to good 1 at the interior utility-maximizing optimum?

$$\frac{\alpha}{\beta} \cdot \frac{p_2}{p_1}$ $$\frac{\alpha}{\alpha + \beta}$ $$\frac{\alpha \cdot p_1}{\alpha + \beta}$ $$\frac{\beta}{\alpha + \beta}$

Correct Answer:

$$\frac{\alpha}{\alpha + \beta}$

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