Description

1 attachmentsSlide 1 of 1attachment_1attachment_1.slider-slide > img { width: 100%; display: block; }

.slider-slide > img:focus { margin: auto; }

Unformatted Attachment Preview

Assignment 3

Econ 3030 Year 2022

1. Consider the following demand functions, which are the result of

maximizing utility where the persons preferences can be represented by a

Cobb-Douglas function.

2

????1 = ????/????1

3

1

????2 = ????/????2

3

a) Use logarithms to show that the demand elasticity (price elasticity of

demand) is equal to 1 for both ????1 ???????????? ????2 .

b) Use logarithms to show that the income elasticity is equal to 1 for both

????1 ???????????? ????2 .

c) What is the cross-price elasticity of good 1 with respect to the price of

good 2?

2. Consider the function ???? = ???? 0.4 ????0.7 , where each variable is a function of

time.

a) Write this in log form.

b) if capital grows at 2% per year and labour grows at 1% per year, what is

the growth rate of Q?

3. Exports, X, are growing at 6%. Imports, M, are growing 7%. At time 0,

exports are 700 and imports are 800.

a) Calculate the growth rate of net exports, NX, where

NX = X M

b) Interpret your result. What does the number you found mean?

4. Challenge level: (though actually very quick)

The elasticity of substitution is defined as percentage change in relative

quantities resulting from a percentage change in the (inverse) relative

????

prices, or the percent change in 1 resulting from a percent change in the

relative price line ????1 /????2 .

????2

Consider the ratio of first order conditions for a Cobb-Douglas utility

optimization problem:

????2

????1

=

1 ????1

4 ????2

Derive the elasticity of substitution for this case.

Purchase answer to see full

attachment

Tags:

economics

demand elasticity

demand functions

User generated content is uploaded by users for the purposes of learning and should be used following FENTYESSAYS.COM ESSAY’s honor code & terms of service.