**Homework 1****1. Convex Preferences, Consumer Equilibrium and Market Demand.**Let $ P_X = \$10 $, $ P_Y = \$15 $, and $ M = \$800 $.1. Find the utility-maximizing consumption bundle for the following utility function: $ U = X^{1/4}Y^{3/4} $. (Hint: use Lagrangian Method to determine $ X^* $, $ Y^* $, and $ U^* $.) Circle your final answers.2. Sketch the demand function for Commodity X in this case. Hint: Express $ P_X $ as a function of X and then put X on the horizontal axis and $ P_X $ on the vertical axis.**Graph Explanation:**The image includes a graph with a grid but no plotted data, titles, or axes labels. The grid is meant to be used for sketching according to the instructions provided. The horizontal axis represents X, and the vertical axis represents $ P_X $.

Answered: 1. Convex Preferences. Consumer…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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**Homework 1**

**1. Convex Preferences, Consumer Equilibrium and Market Demand.**

Let $ P_X = \$10 $, $ P_Y = \$15 $, and $ M = \$800 $.

1. Find the utility-maximizing consumption bundle for the following utility function:
$ U = X^{1/4}Y^{3/4} $. (Hint: use Lagrangian Method to determine $ X^* $, $ Y^* $, and $ U^* $.)
Circle your final answers.

2. Sketch the demand function for Commodity X in this case. Hint: Express $ P_X $ as a function of X and then put X on the horizontal axis and $ P_X $ on the vertical axis.

**Graph Explanation:**

The image includes a graph with a grid but no plotted data, titles, or axes labels. The grid is meant to be used for sketching according to the instructions provided. The horizontal axis represents X, and the vertical axis represents $ P_X $.

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Since you have asked multiple question, we will answer first question for you. If you want any specofic question to be solved then please specify question number or post only that question.

Utility refers to the satisfaction. The aim of any consumer is to maximize the utility. The utility obtained by the consumer depnds on utility function, income and prices of the good.

The indifference curve shows the combination of good that gives the consumer same level of utility.

Budget constraint shows the combination that are affordable by the consumer given the income and prices of the good.

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