4. Suppose the economy has 100 units each of goods X and Y and the utility functions of the (only) 2 individuals are: UA (Xa, YA) pareto-improvement is possible if, initially, goods are divided equally between the two individuals. X0.25 y0.75, UB (XB, YB) = X0.75 y0.25. Show that

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Chapter3: Demand Analysis
Section: Chapter Questions
Problem 2E: The price elasticity of demand for personal computers is estimated to be 2.2. If the price of...
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Given;
0.5Px
Py
0.51
Demand function; Y* =
- 0.5
Py
Here;
Px = 2
Py = 8
I = 96
Therefore:-
0.5(96)
0.5(2)
Y* =
8
- 0.5
8
= * + - 0.5
= 6 + 0. 125 – 0.5
= 5. 625
->
Step 2
Own-price elasticity of demand:-
Py
dY
dPy
メマ
Ed =
0.5Px
Py
0.51
P,2
%D
0.51+0.5Px
Py2
0.5(96)+0.5(2)
82
8
5.625
8
64
5.625
= 1.089
Income elasticity of demand:-
E =
= x +
0.5
0.5
96
5.625
= 1.067
Income elasticity of demand of product Y is greater than 1 which implies that the product is a luxury good. Product X and Y are
related goods, increase in price of product X will increase the demand for product Y.
Transcribed Image Text:Given; 0.5Px Py 0.51 Demand function; Y* = - 0.5 Py Here; Px = 2 Py = 8 I = 96 Therefore:- 0.5(96) 0.5(2) Y* = 8 - 0.5 8 = * + - 0.5 = 6 + 0. 125 – 0.5 = 5. 625 -> Step 2 Own-price elasticity of demand:- Py dY dPy メマ Ed = 0.5Px Py 0.51 P,2 %D 0.51+0.5Px Py2 0.5(96)+0.5(2) 82 8 5.625 8 64 5.625 = 1.089 Income elasticity of demand:- E = = x + 0.5 0.5 96 5.625 = 1.067 Income elasticity of demand of product Y is greater than 1 which implies that the product is a luxury good. Product X and Y are related goods, increase in price of product X will increase the demand for product Y.
3. Suppose that initially Px = 2, Py = 8, 1 = 96 and the Marshallian demand function for
0.SPX - 0.5. Calculate the own price & income
0.51
+
Py
good Y is given by Y* =
elasticities of demand for good Y. Interpret your computed values and say something
about the type of good.
Py
4. Suppose the economy has 100 units each of goods X and Y and the utility functions of the
(only) 2 individuals are: UA (Xa, YA) = X0.25 y0.75, UB (XB, YB) = X0.75 y0.25, Show that
pareto-improvement is possible if, initially, goods are divided equally between the two
individuals.
Transcribed Image Text:3. Suppose that initially Px = 2, Py = 8, 1 = 96 and the Marshallian demand function for 0.SPX - 0.5. Calculate the own price & income 0.51 + Py good Y is given by Y* = elasticities of demand for good Y. Interpret your computed values and say something about the type of good. Py 4. Suppose the economy has 100 units each of goods X and Y and the utility functions of the (only) 2 individuals are: UA (Xa, YA) = X0.25 y0.75, UB (XB, YB) = X0.75 y0.25, Show that pareto-improvement is possible if, initially, goods are divided equally between the two individuals.
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