Ashwin likes to spend her spare time in summer in one of two ways: (i) watching cricket (x) at Sydney Cricket Ground or (ii) watching movies (y) at Ritz cinema. In choosing how to entertain herself, she considers both constraints---money and time. Part I Ashwin has 48 hours of spare time in a month. A cricket game runs for 8 hours, while each visit to the movies takes up 4 hours. Each month, Ashwin also has $324 to spend on entertainment. A ticket for a cricket game costs $45. A visit to the movie costs $36. Write down Ashwin's budget constraint and time constraint. (a) (b) Draw Ashwin's budget constraint and time constraint in a clearly labelled diagram. Label all axis intercepts in the two axes (x and y) and the point of intersection of the two budget lines. Shade the set of bundles that Ashwin can afford (those satisfying both his time and money constraints) with vertical lines.
Ashwin likes to spend her spare time in summer in one of two ways: (i) watching cricket (x) at Sydney Cricket Ground or (ii) watching movies (y) at Ritz cinema. In choosing how to entertain herself, she considers both constraints---money and time. Part I Ashwin has 48 hours of spare time in a month. A cricket game runs for 8 hours, while each visit to the movies takes up 4 hours. Each month, Ashwin also has $324 to spend on entertainment. A ticket for a cricket game costs $45. A visit to the movie costs $36. Write down Ashwin's budget constraint and time constraint. (a) (b) Draw Ashwin's budget constraint and time constraint in a clearly labelled diagram. Label all axis intercepts in the two axes (x and y) and the point of intersection of the two budget lines. Shade the set of bundles that Ashwin can afford (those satisfying both his time and money constraints) with vertical lines.
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.13P
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Transcribed Image Text:a) The s utility function is given as follows:
U(z,y) = x+y
The budget-constrained of 8 in spending money on the watching cricket match and movies as follows:
845x + 36y= 324
Now the utility function for finding the optimal bundle of preferences
The bundle of a and y is under budget
Now the Bundle of (x, y) is (2, 2)
45(2)
36(1)
45x + 36y= 324
36(2) 324
324
162 < 324
The MRS is one means to get an additional unit of zone unit of y will sacrifice and to get one additional unit of y, one unit of z will sacrifice.
The budget line explain if (x, y) is (1, 1)
45(1)
then
=
324
$81 < 324
Now the Bundle of (x, y) is (3, 3)
90+72
Now the Bundle of (x, y) is (4,4)
45x+36y
324
45(3) 36(3) 324
135+108
324
243 < 324
=
U(x, y) = x+y
dU
45x + 36y= 324
45(4) 36(4) 324
180+144
324
324
324
= 1
dz
MU2=1
du
dy
MUy=1
MRS
MUT Pz
MUY Py
MRS=1
=1
MU
MUy
So the optimal bundle for S is 4 unit of z and 4 unit of y that is (4,4).
Transcribed Image Text:Ashwin likes to spend her spare time in summer in one of two ways:
(i) watching cricket (x) at Sydney Cricket Ground or
(ii) watching movies (y) at Ritz cinema.
In choosing how to entertain herself, she considers both constraints---money and time.
Part I
Ashwin has 48 hours of spare time in a month. A cricket game runs for 8 hours, while each
visit to the movies takes up 4 hours. Each month, Ashwin also has $324 to spend on
entertainment. A ticket for a cricket game costs $45. A visit to the movie costs $36.
Write down Ashwin's budget constraint and time constraint.
(a)
(b)
Draw Ashwin's budget constraint and time constraint in a clearly labelled
diagram. Label all axis intercepts in the two axes (x and y) and the point of intersection of the
two budget lines. Shade the set of bundles that Ashwin can afford (those satisfying both his
time and money constraints) with vertical lines.
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