Question

Suppose that the price of a box of crayons is $1 and the price of a box of markers is $2. If maria’s utility function is U = 0.6 C 0.4 M 0.6, where C is the number of crayon boxes and M is the number of marker boxes and her budget is $20.

1. Find the marginal utility of each good
2. Find the marginal rate of substitution
3. How many boxes of crayons and how many boxes of markers should she choose in order to maximize her utility.

Answer 1

SOLUTION:-

U = 0.6 C0.4 M0.6

MUC = U/C = 0.4(0.6 C0.4-1 M0.6) = 0.24C-0.6M0.6

MUM = U/M = 0.6(0.6 C0.4 M0.6-1) = 0.36C0.4M-0.4

MRS = MUC/MUM = 0.24C-0.6M0.6/0.3C0.4M-0.4 = 2M0.6+0.4/3C0.4+0.6 = 2M/3C

Utility is maximizes where MRs = Pc/Pm

So, 2M/3C = 1/2

So, 2M = 3C/2

So, M = 3C/2*2 = 3C/4

So, M = 0.75C

Budget constraint: PcC + PmM income

So, 1*C + 2*(0.75C) = 20

So, C + 1.5C = 2.5C = 20

So, C = 20/2.5 = 8

M = 0.75C = 0.75(8) = 6

Thus, C = 8; M = 6

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