Please explain step by step 7-8-Compute marginal utilities and marginal rate of substitution for each of the utilityfunctions given below.a) U(X,Y) = 1- e-axe-byb) U(X,Y)= XY + 3X + 5Y1c) U(X,Y)= (0.3Xm +0.7Ym)md) U(X,Y)=x1-a y1-b+1-a1-b=Consider an individual who decides to allocate time between different activities.For simplicity suppose that there are two activities: working and leisure. Denoteby tw the time spent for working and to the time spent for leisure and supposethat individual gains utility denoted by U(tw, t₁). Consider that the individual has16 hours a day in total that can be spent for working and/or leisure.a) Discuss possible preferences the individual might have and graphicallyillustrate some examples of indifference curves associated to thesepreferences.b) Graphically illustrate the time constraint the individual faces.c) Graphically illustrate the optimal time allocation of the individual. Explainwhy it is optimal by comparing to a sub-optimal allocation choice.d) Write the optimization problem of the individual (formally, as we wrote inlectures).e) Analytically solve the problem, obtain the necessary condition, and provide aninterpretation of it (explain in your own words what it means).

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Answered: Compute marginal utilities and marginal…

Compute marginal utilities and marginal rate of substitution for each of the utility functions given below. a) U(X,Y) = 1- e-ax - e-by b) U(X,Y)= XY + 3X + 5Y c) U(X,Y)= (0.3Xm +0.7Ym)m 1

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Question

Please explain step by step

7-
8-
Compute marginal utilities and marginal rate of substitution for each of the utility
functions given below.
a) U(X,Y) = 1- e-ax
e-by
b) U(X,Y)= XY + 3X + 5Y
1
c) U(X,Y)= (0.3Xm +0.7Ym)m
d) U(X,Y)=
x1-a y1-b
+
1-a
1-b
=
Consider an individual who decides to allocate time between different activities.
For simplicity suppose that there are two activities: working and leisure. Denote
by tw the time spent for working and to the time spent for leisure and suppose
that individual gains utility denoted by U(tw, t₁). Consider that the individual has
16 hours a day in total that can be spent for working and/or leisure.
a) Discuss possible preferences the individual might have and graphically
illustrate some examples of indifference curves associated to these
preferences.
b) Graphically illustrate the time constraint the individual faces.
c) Graphically illustrate the optimal time allocation of the individual. Explain
why it is optimal by comparing to a sub-optimal allocation choice.
d) Write the optimization problem of the individual (formally, as we wrote in
lectures).
e) Analytically solve the problem, obtain the necessary condition, and provide an
interpretation of it (explain in your own words what it means).

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