Question

A consumer uses her available income to buy rice and gasoline. Her indifference curves and budget constraint are shown on the diagram to the right. What is the marginal rate of transformation (MRT) facing this consumer?

At point C the marginal utility per dollar spent on rice is _______ the marginal utility per dollar spent on gasoline.

Answer 1

The two points on the budget lines are \((0,40)\) and \((30,0)\).

The slope of the budget line is as calculated below.

$$ \begin{aligned} \text { Slope } &=\frac{0-40}{30} \\ &=-\frac{4}{3} \end{aligned} $$

Thus, the marginal rate of transformation is \(\frac{4}{3}\).

At point \(\mathrm{C}\), the marginal rate of substitution is lesser than the marginal rate of transformation.

$$ \begin{aligned} &M R T>M R S \\ &\frac{4}{3}>\frac{M U_{R}}{M U_{G}} \end{aligned} $$

Thus, the marginal utility per dollar spent on rice is smaller than the marginal utility per dollar spent on gasoline. Decreasing the consumption of rice and increasing the consumption of gasoline would enable to increase the utility.