Economics Homework, please help!

[Bigblades]

So we get a question about maximizing the utility of pizza and beer. pizza is $ 6 and beer is $ 1.5 , if a budget constraint is $ 18000 maximize the utility.

That part is straightforward, the Utility fucntion is Z * B so zb = U

6z +1.5b = 18000 Marginal rate of substitution is 4b = 1z

Substitute that in you get 6z + 1.5 (4z) = 18000
Z = 1500 and B = 6000 for max utility.


Now, on the second part its harder, cause it says instead the util function is U = zb + 432

How does that affect the amount of each that you want? It either has no effect on the MRS and the amount consumed is the same, or it makes it so that the Marginal rate of substitution is
4(b+ 432) = z + 432 instead, and the problem is worked accordingly. Which one is it?

Third part we just.. didn't know how to do.

It is suppose that the person is offered either a cash gift of $12000 or 8000 more beers. Which would they prefer and why? How do you work it to find which is better? I can work it for the cash gift as that would just change the budget constraint to $30000, but how would you figure out the new amounts consumed if 8000 beers are added? How does that change the marginal rate of substitution or how do you add 8000 beers into the equation to figure how that changes utility?



Please help me. Will give cookies and beer to person with best answer. Also possibly cash gift depending on how much is in my account and if I remember my paypal password.

 

[yobarman]

You know for an ecomics minor I should know these things. Oh well... I've moved on to harder things like Industrial Organization

 

[HappyPuppy]

No.

 

[b0mbrman]

Originally posted by: Bigblades
Now, on the second part its harder, cause it says instead the util function is U = zb + 432

Why should it be different? When you derive it, that 432 just disappears. It just shifts the entire utility curve up 432...in real life terms, when you have no pizza or beer, you've got some joy whereas before, you had none

Third part we just.. didn't know how to do.

It is suppose that the person is offered either a cash gift of $18000 or 8000 more beers. Which would they prefer and why? How do you work it to find which is better? I can work it for the cash gift as that would just change the budget constraint to $30000, but how would you figure out the new amounts consumed if 8000 beers are added? How does that change the marginal rate of substitution or how do you add 8000 beers into the equation to figure how that changes utility?

You're going to compare two max utilities...

a) The budget constraint is now $36,000 (Or am I missing the reason you only made it $30k?) so just solve the way you did before
b) now, the utility you are trying to maximize is z(b+8000)

That's the way I see it...I could, of course, be absolutely wrong as I'm a couple years out of practice

 

[UncleWai]

No effect on Marginal Utility. If you find the derivate, the 432 disappears.
The third question, 8000 * $1.5 = $12000 worth of beer, of course $16000 > $12000
THe $16000 cash will push the budget constraint out so the intercepts are 34000/1.5 beer or 34000/4 pizzas.
The beer Q will just be horizontal for 8000 in the beginning, and then goes down like it normally would.
pizza
|_____
|.........\
|..........\
|............\
|________\______________
..........|.....|
8000 original +8000

By the way, this is intermediate econ, advanced econ is some messed up stuff.

*god damn space doesn't work for my l33t ASCII skill

 

[b0mbrman]

Originally posted by: UncleWai
By the way, this is intermediate econ, advanced econ is some messed up stuff.

Agreed

 

[iamme]

Originally posted by: b0mbrman

Originally posted by: UncleWai
By the way, this is intermediate econ, advanced econ is some messed up stuff.

Agreed

yup, this is the "Managerial" Econ (right after macro and micro) at our school.

sadly, i retained none of what i learned.

 

[Bigblades]

Oops, correction, the cash gift is 12000, not 18000. Editing to fix now. Sorry about that...

 

[b0mbrman]

Originally posted by: Bigblades
Oops, correction, the cash gift is 12000, not 18000. Editing to fix now. Sorry about that...

Alright...doesn't change my answer much (or rather, my intermediate answer )

You're comparing the max utilities of

a) Budget constraint of $30,000

vs.

b) U = z(b+8000)

 

[UncleWai]

I knew it.
Either, you will still take the cash because it gives you more choice.
Because with beers, you are stucked with 8000, so your decision in buying pizzas are unchanged.
But with the $12000, you have more combinations.

 

[Bigblades]

a) The budget constraint is now $36,000 (Or am I missing the reason you only made it $30k?) so just solve the way you did before
b) now, the utility you are trying to maximize is z(b+8000)


How do you work the problem with it as z(b+8000)? What does the new equation look like?

 

[her209]

Can we say it yet?

Fo...

 

[Albis]

sigh having taken intermediate econ a few terms ago. i remember close to enough

i am good at economic theory but this basic math / grinding stuff always tricks me

 

[b0mbrman]

Originally posted by: Bigblades
How do you work the problem with it as z(b+8000)? What does the new equation look like?

solve for b using the $18k constraint.
substitute into U = z(b+8000)
Derive
Set equal to 0 to find max utility

 

[5LiterMustang]

Originally posted by: b0mbrman

Originally posted by: Bigblades
Now, on the second part its harder, cause it says instead the util function is U = zb + 432

Why should it be different? When you derive it, that 432 just disappears. It just shifts the entire utility curve up 432...in real life terms, when you have no pizza or beer, you've got some joy whereas before, you had none

Third part we just.. didn't know how to do.

It is suppose that the person is offered either a cash gift of $18000 or 8000 more beers. Which would they prefer and why? How do you work it to find which is better? I can work it for the cash gift as that would just change the budget constraint to $30000, but how would you figure out the new amounts consumed if 8000 beers are added? How does that change the marginal rate of substitution or how do you add 8000 beers into the equation to figure how that changes utility?

You're going to compare two max utilities...

a) The budget constraint is now $36,000 (Or am I missing the reason you only made it $30k?) so just solve the way you did before
b) now, the utility you are trying to maximize is z(b+8000)

That's the way I see it...I could, of course, be absolutely wrong as I'm a couple years out of practice

I think you're correct...I have taken lots of econ classes an dominated them but I'm also a couple years out of date...but I think you're correct.

 

[dbk]

oh god I hate micro... :heart: macro

 

[Bigblades]

I agree with everybody's conclusion on part B, my buddy here and I weren't really sure on that one, he thought that you had to take the partial derivative and leave the 432 on there. I thought that it didn't have an affect on the util.

Part C I'm not sure what the subsitution would looke like

In A it was 6z + 1.5b = 18000 so 4b = z so you substitute 6z + 1.5(4z) = 18000

6z + 1.5(8000+b) = 18000, so the substitution relation is different, its no longer 4x as much.. but I dunno what it is.. I just know that its not 6z + 1.5(4(8000+b) = 18000. What would it look like?

 

[b0mbrman]

Originally posted by: Bigblades
I agree with everybody's conclusion on part B, my buddy here and I weren't really sure on that one, he thought that you had to take the partial derivative and leave the 432 on there. I thought that it didn't have an affect on the util.

Part C I'm not sure what the subsitution would looke like

In A it was 6z + 1.5b = 18000 so 4b = z so you substitute 6z + 1.5(4z) = 18000

6z + 1.5(8000+b) = 18000, so the substitution relation is different, its no longer 4x as much.. but I dunno what it is.. I just know that its not 6z + 1.5(4(8000+b) = 18000. What would it look like?

You don't have to pay for those 8000 extra beers so you'd still be using 6z + 1.5b = $18000 as your uh...consumption possibilities frontier (i might have just made up that name)

The 8000 beers only come into play for utility...U = z(b+8000)