**Perfect Substitutes**Suppose that Jason’s utility is entirely based on the number of hours of skiing (X) and skating (Y). His utility function is as follows:\[ U(X,Y) = 5X + 3Y \]1. **Sketch Jason’s indifference curves.** *Explanation:* The indifference curves represent combinations of skiing and skating that provide Jason with the same level of utility. Since the utility function is linear, the indifference curves will be straight lines. Each curve can be obtained by setting $ U(X,Y) $ to a constant value and solving for Y in terms of X. For example, if $ U(X,Y) = k $, then $ 3Y = k - 5X $ or $ Y = \frac{k}{3} - \frac{5}{3}X $. This is a line with a slope of $-\frac{5}{3}$.*Graph:* There is a grid with a set of horizontal and vertical lines representing axes for quantities of skiing (X-axis) and skating (Y-axis). Plot straight lines with a slope of $-\frac{5}{3}$ to illustrate indifference.2. **What is Jason’s marginal rate of substitution (MRS) between skiing and skating?** *Explanation:* The marginal rate of substitution is the rate at which Jason is willing to substitute skiing for skating while maintaining the same level of utility. It is calculated as the negative of the ratio of the marginal utilities of the two goods. Thus, the MRS is equal to $-\frac{MU_X}{MU_Y} = -\frac{5}{3}$.In this scenario, Jason can trade off $\frac{5}{3}$ hours of skiing for 1 hour of skating, keeping his utility constant.

An indifference curve depicts the combination of two goods that derives the same level of utility.…

Answered: Suppose that Jason's utility is…

Suppose that Jason's utility is entirely based on number of hours of skiing (X) and skating (Y). His utility function is as follows: U (X,Y)= 5X + 3Y 1. Sketch Jason's indifference curves.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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