Economics Questions

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.
𝑥𝑥1 = 2
3
𝐵𝐵/𝑃𝑃1 𝑥𝑥2 = 1
3
𝐵𝐵/𝑃𝑃2
a) Use logarithms to show that the demand elasticity (price elasticity of
demand) is equal to 1 for both 𝑥𝑥1 𝑎𝑎𝑎𝑎𝑎𝑎 𝑥𝑥2.
b) Use logarithms to show that the income elasticity is equal to 1 for both
𝑥𝑥1 𝑎𝑎𝑎𝑎𝑎𝑎 𝑥𝑥2.
c) What is the cross-price elasticity of good 1 with respect to the price of
good 2?
2. Consider the function 𝑄𝑄 = 𝐾𝐾0.4𝐿𝐿0.7, 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 𝑥𝑥1
𝑥𝑥2
resulting from a percent change in the
relative price line 𝑝𝑝1/𝑝𝑝2.
Consider the ratio of first order conditions for a Cobb-Douglas utility
optimization problem:
𝑥𝑥2
𝑥𝑥1
= 1
4
𝑝𝑝1
𝑝𝑝2
Derive the elasticity of substitution for this case.