Question

3. Assume and individual has the following utility function:
U= 5F+2C
If food costs $8/unit and clothing costs $25/unit, how much of each will an individual with an income of
$1000 purchase? If the price of all goods double, by how much will the individual’s income need to be
increased to leave utility unchanged?

Answer 1

The utility function represents food and clothes as perfect substitutes of each other for the consumer and hence the indifference curves are downward sloping straight lines. On the other hand, the budget line is also negatively sloped straight line, which has vertical intercept as 40 and horizontal intercept is 125, if food is represented in x-axis and clothes are represented in y-axis.

In case of substitutes, since price of food ($8 per unit) is less than the price of clothes ($25 per unit), the consumers will specialize in consuming food. Hence, the consumer will maximize on the food axis, where the budget constraint meets the downward sloping indifference curve and spend all the income on food. Hence, an individual will consume 1000/8 = 125 units of food and no consumption of cloth.

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Consider now prices of both the goods get double. In order to keep the utility level same, the optimal solution has to be at the point where budget line and indifference curves were meeting, i.e., food = 125. In other words, the budget line must not change from its original position. When the prices of both the goods get double, the only way the budget line remains same is by doubling the income. If we double the income level also, the horizontal as well as vertical intercept remain same and the budget line does not change at all.