List of top Microeconomics Questions on Utility Function asked in IIT JAM EN

In a two-good world, the utility function of a consumer is given by

The utility function of a consumer in a two-good world is given by

An industry has 6 firms in Cournot competition. Each of the 6 firms has zero fixed costs, and a constant marginal cost equal to 20. The product is homogenous and the industry inverse demand function is given by 𝑃 = 230 − 𝑄, where 𝑃 is the market price and 𝑄 is the industry output (sum of outputs of the 6 firms). The market price under Cournot-Nash equilibrium is equal to _____ (in integer).

A consumer’s utility function is given by: $𝑢(𝑥_1, 𝑥_2) = (2𝑥_1 − 1)0.25(𝑥_2 − 4)0.75$ If the consumer has a budget of 73 and the unit prices of $𝑥_1$ and $𝑥_2$ are given by 2 and 1, respectively, then the value of ($𝑥_1 + 𝑥_2$) is ________ (rounded off to two decimal places).

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?