Question

The consumer's budget constraint is $6 = 0.50G + P, where G is packs of gum and P is bags of pretzels. The marginal utility of pretzels is MUP = G0.5, and the marginal utility of gum is MUG = 0.5G–0.5P. The consumer's utility function is U = G0.5P. the utility-maximizing bundle consists of _____ packs of gum and _____ bags of pretzels.

6; 3

2; 5

4; 4

8; 2

Answer 1

4; 4

Explanation:
U = G^0.5P

From the budget constraint, price of G is Pg = $0.50; Price of P is Pp = $1; and income (M) = $6

Utility is maximized at the point where MRS = Pg/Pp
MRS = MUG/MUP = (0.5G^-0.5P)/(G^0.5) = 0.5P/G^0.5+0.5 = 0.5P/G

So, 0.5P/G = 0.5/1
So, P = (0.5G)/0.5 = G
So, P = G

Now, substituting it in the budget constraint, we get,
6 = 0.50G + G = 1.5G
So, G = 6/(1.5) = 4

Thus, P = G = 4