Question

Using the utility function U(x,y)=3x+y/2, px=7, py=1, and M=46 , what is the utility-maximizing demand for y, y*?

Answer 1

Maximize : U = 3x + y/2

Subject to : 7x + 1y = M = 46 -----------------Budget Contraint

We can see from above that It considers x and y as perfect substitutes and values x, 3(2) = 6 times over y.

Thus for this problem utility maximizing Condition will be :

(i) If px < 6py, He will consume only x.

(ii) If px < 6py, He will consume only y

(iii) If px < 6py, He will consume that lies on the above budget line.

Here, px = 7 > 6py. Thus will condume only y. So we have x = 0.

Putting this in budget constraint we get :

7*0 + y = 46 => y = 46

Thus utility maximizing demand for y is y = 46 units