# Demand Functions Worksheet

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Assignment 3
Econ 3030 Year 2022
1. Consider the following demand functions, which are the result of
maximizing utility where the persons 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.

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Tags:
economics

demand elasticity

demand functions

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