All income of $1,000 is spent on Books and clothing.  Book is $100 per
unit and Clothing is $500 per unit
                     Marginal Utility
No. Units of	     	        
Good consumed      Books    Clothing

1	  	     20         50	
2	      	     18		45
3	      	     16		40
4	      	     13		35
5	      	     10		30
6	       	      6	        25
7	       	      4	        20
8	       	      2	        15

With only $1,000 income per month how many units of each should be
purchased?

down,

The way I'd normally approach a problem like this is to draw a nice
diagram with Books on one axis and Clothing on the other axis and go
from there. But it's a little difficult to do that in a text box, so
imagine a diagram (always impresses the professor if you do it right -
picture worth a thousand words and all that...)

First of all, what are the feasible combinations of books and
clothing? I.e. what is the budget constraint.

Mathematically we have :

100 * Books + 500 * Clothing = 1000

So we can buy anywhere from 10 books and no clothes (yikes) to no
books and 2 clothes (at least you'd look cool).

This is a straight line with slope 1/5 (assuming books are on your
x-axis and clothing is on your y-axis). It has to pass through the
coordinates (10,0) and (0,2) (if you're following along at home with
the diagram).

Now our optimal bundle of clothes and books is the combination that
makes us indifferent between buying $0.01 (a really small amount) of
books (instead of clothes) and buying $0.01 worth of clothing (instead
of books). You can be a little more technical about it (depends at
what level the question is being done - some courses require a brief
essay in calculus, others are happy for you to just repeat the
following sentence) but in essence you want to find

"the point at which MU(books)/MU(clothing) = slope of budget line =
Price(books)/Price(clothing)"

You draw this on your diagram by drawing a curve that is tangential
(just touches) your budget line.

So in this particular question we want MU(books)/MU(clothing) to be
1/5.

When x = 0 (no books), y = 2 (2 clothes). MU(books) is 0 and
MU(clothes) is 45, so the slope is 0/45 = 0.
When x = 5, y = 1. MU(books) is 10 and MU(clothes) is 50 so the slope
is 10/50 = 1/5.

This is the slope we are looking for, so the solution to the question
is to spend $500 on books and $500 on clothes.

This should be the kind of level that the question requires (assuming
the course is econ 101/102 or even econ 151), but if you think that
I've oversimplified the explanation I can give you the technical
solution (Econ 201 or higher) involving calculus and plotting the
indifference curves (a bit of an overkill for this question).

Kind Regards

calebu2-ga

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