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Suppose the two goods, X1 and X2, are perfect substitutes at the ratio of 1 to...

Suppose the two goods, X1 and X2, are perfect substitutes at the ratio of 1 to 2 – each unit of X1 is worth, to the consumer, 2 units of X2. The consumer had an income of $100. P1=5, and P2=3. Find the optimal basket of this consumer.

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Answer #1

According to the information given the utility function is U = 2X1 + X2

this implies that the marginal rate of substitution which is the ratio of the marginal utilities of the two goats, is -2/1 or -2. Slope of the budget constraint is -p1/p2 or -5/3.

In absolute terms, marginal rate of substitution is greater than the slope of the budget constraint which means X1 generates more utility than X2.

At the optimal consumption bundle only X1 is consumed. It is equal to 100/5 or 20 units

Optimal consumption basket has 20 units of X1 and no units of X2.

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