You are planning a budget for the region of Tirana The two m

You are planning a budget for the region of Tirana. The two major budget positions include education (Z) and health care (w). Your preferences over the two are represented by function:   U (Z, W) = 3Z + W

a. Please state what type of utility/preferences is the above function

b. Find the marginal rate of substitution

c. Find optimal consumption of Z and W given PZ =2, PW=1 and m=50

Solution

A.

The given utility function is the example of perfectly substitutes utility function. Here, Z and W can be substituted using some multiples of the quantity with each other.

B.

Marginal rate of substation (MRS) = MUz/MUw

U = 3Z + W -------------- (1)

Differentiation of eq. 1 w.r.t. Z will give MUz.

MUz = 3

Differentiation of eq. 1 w.r.t. W will give MUw.

MUw = 1

So,

MRS = MUz/MUw

MRS = 3/1 = 3

C.

M = 50 = Pz*Z + Pw*W

50 = 2*Z + 1*W

As per the MRS,

3Z = W

50 = 2Z + 3Z

Z = 10

W = 30

So, optimal combination will be, Z = 10 and W = 30.