Question

Consider the following three utility functions:
$F = (4x_1 + 2x_2), G = min (4x_1, 2x_2)$ and $H = (\sqrt{x_1} + x_2)$ where, $x_1$ and $x_2$ are two goods available at unit prices $p_{x1}$ and $p_{x2}$ , respectively. Which of the following is/are CORRECT for the above utility functions?

• A. The marginal rate of substitution is given by −1, −2, and $−0.5\sqrt{x_1}$ for the utility functions F, G, and H, respectively
• B. If $p_{x1}$ = $p_{x2}$, then the utility maximisation problem with utility function 𝐹 has a corner solution
• C. If income is 100 and $p_{x1}$ = $p_{x2}$ = 2, then in the utility maximisation problem with utility function G, the sum of the optimal values of $x_1$ and $x_2$ is 50
• D. If income is 100, $p_{x1}$ = 5, and $p_{x2}$ = 5000, then in the utility maximisation problem with the utility function H, the optimal value of $x_2$ is 20

Answer 1

Answer: (B), (C)

If $p_{x1}$ = $p_{x2}$, then the utility maximisation problem with utility function 𝐹 has a corner solution

Answer 2

The correct Options are B and C : If $p_{x1}$ = $p_{x2}$, then the utility maximisation problem with utility function F has a corner solution AND If income is 100 and $p_{x1}$ = $p_{x2}$ = 2, then in the utility maximisation problem with utility function G, the sum of the optimal values of $x_1$ and $x_2$ is 50