Question

Question 7 Consider a consumer with preferences over two goods 1 and 2. Assume that the horizontal axis pertains to the amount of good 1 and the vertical axis pertains to the amount of good 2. Suppose that, given the consumption bundle r = 10 and y = 10, a consumer's MRS (marginal rate of substitution) is equal (in absolute value) to 4. The price of good 1 is $1, the price of good good 2 is $0.25, and the consumer's income is $12.5. The consumer's preferences are strictly convex. Which of the following is true? (A) To maximize utility the consumer should buy less of good 1 and more of good 2. (B) To maximize utility the consumer should buy more of both good 1 and good 2. (C) To maximize utility the consumer should buy more of good 1 and less of good 2. (D) The bundle x = 10 and y = 10 maximizes the consumer's utility.

can you please explain this deeply? thank you

Answer 1

MRS = 4

P₁/P₂ = 1/0.25 = 4

The utility maximization condition is MRS=MU1/MU2 = P1/P2.

And here , MRS= P1/P2 . This implies that the given bundle x=10 and y=10 maximizes the consumer's utility . That is , the indifference curve is tangent to the budget line.

It is given that consumer's income= $12.5

Here we can see that with the given bundle , consumer exhausts all the given income.

($1)(10)+ ($0.25)(10) = $12.5 which satisfies the budget constraint condition also.

Hence,option(D) is correct.