Douglas' utility function is u = min{2x₁, x₁ + x₂}. Suppose the prices and income are (p₁, P2, m) = (1, 2, 20). Then his utility-maximizing consumption of the first good is units and of the second good is units. Suppose the prices and income are (p1, p2, m) = (1, 1, 20). Then his utility-maximizing consumption of the first good is units and of the second good is units.

Micro Economics For Today
10th Edition
ISBN:9781337613064
Author:Tucker, Irvin B.
Publisher:Tucker, Irvin B.
Chapter6: Consumer Choice Theory
Section: Chapter Questions
Problem 11SQ
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Douglas' utility function is u =
min{2x₁, x₁ + x₂}.
Suppose the prices and income are (p₁, P2, m) = (1, 2, 20).
Then his utility-maximizing consumption of the first good is
units and of the second good is
units.
Suppose the prices and income are (p1, p2, m) = (1, 1, 20).
Then his utility-maximizing consumption of the first good is
units and of the second good is
units.
Transcribed Image Text:Douglas' utility function is u = min{2x₁, x₁ + x₂}. Suppose the prices and income are (p₁, P2, m) = (1, 2, 20). Then his utility-maximizing consumption of the first good is units and of the second good is units. Suppose the prices and income are (p1, p2, m) = (1, 1, 20). Then his utility-maximizing consumption of the first good is units and of the second good is units.
Expert Solution
Step 1: Utility Function - Introduction

Given Utility Function : U=min{2x1,x1+x2}

It is a complementary utility function where two goods are consumed together. Consuming only one good will give no utility to the consumer.

So, 2x1=x1+x2

2x1-x1=x2

x1=x2

Now, we will substitute the above-obtained equation in the budget line.

A budget line represents the combination of goods that can be consumed given prices and income.

BL: p1x2+p2x2=M

Given:

p1=1

p2=2

M=20

1x1+2x2=20

Since, x1=x2

x1+2x1=20

3x1=20

x1*=20/3=6.67

x2*=6.67


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