A student has a monthly budget of $800. She can spend her budget on two items, X and Y. Each unit of X costs $20 and each unit o
f Y costs $10. If the student has a utility function of U = 348X + 100Y + 6X2 + 4Y2 + 2XY, what is the optimal amount of X and Y for her to consume to have the maximum utility? What is this total utility? What is the value of lambda and what does this mean?
1 answer:
Answer:
Check the explanation
Step-by-step explanation:
Total utility is the overall satisfaction that a particular consumer received from consuming a given overall quantity of a good or service, To calculate the value of total utility economists utilize the following basic total utility formula: TU = U1 + MU2 + MU3
Kindly check the attached image below to see the step by step explanation to the question above.
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Answer:
a)
S+G=525
G=S+75
b) See attached pictures
c) S=$225 and G=$300
The point where both graphs meet each other is the point where both equations will be true when having the same S and G values. This is, this is the point where both conditions given by the problem are the same.
Step-by-step explanation:
a) For the first part of the problem, the addition of both amounts will give us the total, so the first equation is:
S+G=525.
On the second equation we need to add 75 to sharon's amount to figure Geordi's amount, so we get:
G=S+75
b) In order to graph the system of equations, we need to find two points for each of the equations. It would be a good idea to solve the first equation for g, so our system of equations would be:
G=525-S
G=S+75
First Equation:
You can pick any value you like for S, for example: S=0 and then substitute it into the equation to get te first G-value:
G=525-0
so G=525.
So the first ordered pair would be (0,525)
You can do the same with a different S-value to get a second point to plot:
S=100
G=525-100
G=424
so the second ordered pair would be (100,424)
and now you can plot the points on the graph and connect them with a straight line.
See attached picture.
Second Equation:
The same procedure is followed for the second equation, in this case I used the same S-values, but you can use different values if you wish, so the two points to plot were:
(0,75)
(100,175)
and the graph looks like the one attached.
c)
In order to figure out how much each person earned, we need to find the point where the two graphs meet each other (see attached picture) in this case the point will be located at (225,300)
This means that Sharon earned a total of $225 while Geordi earned a total of $300.
S=$225 and G=$300
The point where both graphs meet each other is the point where both equations will be true when having the same S and G values. This is, this is the point where both conditions given by the problem are the same.
