# Math Help - Demand and Utility Question

1. ## Demand and Utility Question

I have a perplexing practice problem:

A consumer can spend all her money on books (x) or films (z).

Her budget constraint is given as 10x + 20z =200

and utility is $U(x,z)=x^{.5}z^{.25}$

What happens if her money is increased to 250? Why? What does that mean?

From what I can tell, the current optimization (taken by setting the constraint as x=20-2z and plugging it into the utility function, taking the derivative, and setting it equal to zero) is x= 13.34 and z= 3.33

If the budget increases by 50, the consumption will increase too, but what calculation should I use? And what will I be looking at? The marginal rate? I don't understand what I can calculate to show change as the budget increases.

2. From what I can tell, the current optimization (taken by setting the constraint as x=20-2z and plugging it into the utility function, taking the derivative, and setting it equal to zero) is x= 13.34 and z= 3.33
Yes. If you are comfortable with algebra, You could instead use the constraint x = 0.1Y -2z. This will let you calculate the demand for x,z in terms of the amount of any income level (Y). Then just substitute Y=200 and Y=250 into your demand function to help you answer the rest of the question.