Suppose that there are two goods, X and Y. The utility function is U = X^0.5Y. The price of X is P, and the price of Y is $4. Income is $120. The demand for X as a function of P is x =____.

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Quizplus · Accepted Answer

The utility function appears to be incorrectly formatted, but assuming a typical utility maximization problem under a budget constraint, the demand function for good X can be derived using the budget constraint $PxX + 4Y = 120$. Without specific utility function details, a common approach is to allocate spending proportionally based on prices and preferences. Given the lack of specific preference information, if we assume a simple case where all income is spent and preferences are such that the demand for X inversely depends on its price, the demand function $x = \frac{Income}{P} \times \frac{1}{Price\ of\ Y}$ simplifies to $x = \frac{120}{P}$ given the price of Y and total income. Among the provided options, $A) 40/P$ is the closest in form, suggesting a scenario where a quarter of the income is allocated to purchasing X, which is a plausible scenario given certain utility functions and assuming the rest of the income is allocated to Y or other goods. This is a simplified explanation and the exact demand function would depend on the specific form of the utility function and the solution to the consumer's optimization problem.

Suppose That There Are Two Goods, X and Y