Question

A utility function is given as U = √MB

where B represents the quantity of books consumed and M represents magazines. This utility is shown via indifference curves in the diagram to the right.

 

If the quantity of books is held constant at 20 units, then the loss in utility by giving up 10 magazines bundle V to P) is _______ (and do not include a minus sign)

 

How many additional books are necessary to compensate the consumer for this loss in magazines such that total utility is the same as at point V? _______ units. (Enter your response as an integer)

 

Use the point drawing tool to show this bundle. Label this point 'R' Carefully follow the instructions above, and only draw the required object.

Answer 1

a) When 20 books and 10 magazines are consumed (point P), total utility derived from such bundle is:

U = (MB)^1/2 = (20*10)^1/2 = 14.142

and when 20 books and 20 magazines are consumed (point V), total utility derived from such bundle is:

U = (MB)^1/2 = (20*20)^1/2 = 20

Thus utility reduced from point V to P is 20 - 14.142 = 5.858.

b) To get same utility level of V that is 20 utils, we would need to increase units of books in such way that product of books and magazines becomes 400.

Now we have 10 magazines, thus to make it 400 with a product we need 40 as a product.

thus 40 - 20 = 20 more additional books will be required to have same utility level of point V.

Point R will shown at coordinate (40,10) that is 40 books and 10 magazines.