Respuesta :
Answer:
The total effect is 35 out of which income effect is 15 and substitution effect is 20.
Explanation:
Ross has an income of $1440.
The price of chocolates (Px) is $10 and donuts (Py) is $9.
The utility function is given as
U = 0.5xy
Before price rise, Budget line:
1440 = 10x + 9y,
Consumption is optimal when
[tex]\frac{MUx }{ MUy} = \frac{Px}{Py} = \frac{10}{9} = 1.11[/tex]
0.5y / 0.5x= 1.11
y = 1.11x
Substituting in budget line,
1440 = 10x + 9y = 10x + 9(1.11x)
1440 = 10x + 9.99x
19.99x = 1440
x = 72
y = 1.11x = 79.92 = 80
After price rise,
Py = 16.
New budget line:
1440 = 10x + 16y,
Price ratio
[tex]\frac{Px}{Py } = /[/tex]
=[tex]\frac{10}{16}[/tex]
= 0.625
And,
[tex]\frac{MUx}{Muy} = \frac{0.5y}{0.5x} = 0.625[/tex]
[tex]\frac{y}{x} = 0.625[/tex]
y = 0.625x
Substituting in new budget line: 1440 = 10x + 16y
1440 = 10x + 16(0.625)x
1440 = 20x
X = 72
Y = 0.625x = 45
So, total effect (TE)
= Decrease in consumption of y
= 80 - 45
= 35
With previous (x, y) bundle,
U = 0.5xy
U = 0.5 x 72 x 80
U = 2880
Keeping utility level the same & substituting,
y = 0.625x in utility function:
28800 = 0.5xy
[tex]2880 = 0.5\ \times\ 0.625x[/tex]
[tex]2880 = 0.3125x^{2}[/tex]
[tex]x^{2} = \frac{2880}{0.3125} [/tex]
[tex]x^{2} = 9216[/tex]
[tex]x = \sqrt{9216}[/tex]
x = 96
Now, putting the value of x,
y = [tex]0.625\ \times\ x[/tex]
y = [tex]0.625\ \times\ 96[/tex]
y = 60
Substitution effect (SE)
= 80 - 60
= 20
Income effect
= TE - SE
= 35 - 20
= 15
