You have $20 per week to spend, and two possible uses for this money:
telephoning friends back home, and drinking coffee. Each hour of phoning costs $2, and each cup of coffee costs $1. Your utility function is U(X,Y) = XY, where X is the hours of phoning you do, and Y the number of cups of coffee you drink. (X and Y are continuous variables. Interpret fractions as averages over several weeks.)
(a) What are your optimal choices? What is the resulting utility level? You can
use the standard result on the constrained maximization of such a function, but must state it clearly.
(b) Now suppose the price of telephone calls drops to $1 per hour. What are your
optimal choices? What is the resulting utility level?
(c) How much income per week will enable you to achieve the same quantities at
the new prices as the ones you chose before? What income will enable you to attain the same utility as you did before? Which amount is smaller, and why?
Answers
Answer:
You have $20 per week to spend, and two possible uses for this money:
telephoning friends back home, and drinking coffee. Each hour of phoning costs $2, and each cup of coffee costs $1. Your utility function is U(X,Y) = XY, where X is the hours of phoning you do, and Y the number of cups of coffee you drink. (X and Y are continuous variables. Interpret fractions as averages over several weeks.)
(a) What are your optimal choices? What is the resulting utility level? You can
use the standard result on the constrained maximization of such a function, but must state it clearly.
(b) Now suppose the price of telephone calls drops to $1 per hour. What are your
optimal choices? What is the resulting utility level?
(c) How much income per week will enable you to achieve the same quantities at
the new prices as the ones you chose before? What income will enable you to attain the same utility as you did before? Which amount is smaller, and why?(a) Length =10cm, breadth =8cm, height =3cm
Volume of cuboid =lbh=10×8×3=240cm
3
[V=240cm
3
]
(b) Length =1.5m, breadth =25cm, height =15cm
[1m=100cm]
Volume of cuboid =lbh=150×25×15=56250
[V=56,250cm
3
]
(c) Length =15cm, breadth=2.5dm, height =8cm
[1dm]=10cm
Volume of cuboid =lbh=15×25×8
[V=3000cm
3
].
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(a) Length =10cm, breadth =8cm, height =3cm
Volume of cuboid =lbh=10×8×3=240cm
3
[V=240cm
3
]
(b) Length =1.5m, breadth =25cm, height =15cm
[1m=100cm]
Volume of cuboid =lbh=150×25×15=56250
[V=56,250cm
3
]
(c) Length =15cm, breadth=2.5dm, height =8cm
[1dm]=10cm
Volume of cuboid =lbh=15×25×8
[V=3000cm
3
].
verified_toppr
Answer verified by Toppr
View
10834 Views