Thank you for visiting Hendrick consumes coffee and tea The local store has a special pricing policy for coffee if you buy tex x tex servings of coffee you. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Hendrick's utility function can be represented as u(x, y) = 3x + y, where x represents the consumption of coffee and y represents the consumption of tea.
In the utility function u(x, y) = 3x + y, the coefficient 3 in front of x indicates that Hendrick derives three times more utility from consuming coffee compared to tea. The utility function assumes that the caffeine content is the sole source of utility for Hendrick.
In terms of budget allocation, Hendrick's budget constraint can be expressed as 2√x + y = 15, considering the pricing policy for coffee and the fixed price of tea. This equation represents the combinations of coffee (x) and tea (y) that Hendrick can purchase given his budget of $15.
To determine the optimal bundle, we need to find the combination of coffee and tea that maximizes Hendrick's utility function u(x, y) = 3x + y, while still satisfying the budget constraint. This can be achieved by finding the tangency point between an indifference curve representing the utility function and the budget constraint line.
The optimal bundle occurs at the point where the budget constraint line is tangent to the highest possible indifference curve, indicating the maximum level of utility given the budget constraint.
At this point, the marginal rate of substitution (MRS) between coffee and tea, which represents the willingness of Hendrick to substitute one good for another while maintaining the same level of utility, is equal to the price ratio of the two goods.
The utility function represents the preferences of an individual and is used to measure the satisfaction or happiness derived from consuming different goods. In this case, Hendrick's utility function is linear, indicating that the marginal utility of coffee is constant (3) and the marginal utility of tea is 1.
The budget constraint helps determine the feasible combinations of coffee and tea that Hendrick can purchase with his limited budget. By finding the optimal bundle, we identify the combination of coffee and tea that maximizes Hendrick's utility given his budget constraint.
This analysis is based on the assumption that Hendrick's preferences can be adequately represented by the utility function and that he is a rational consumer seeking to maximize his overall satisfaction.
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