Question

Assume that the prices of good X, Y and Z are as follows R5, R1 and R4 respectively, and the Judith has an income of R37 to spend. How much of each good will Judith consume in order to maximise her utility? What will be her total utility and marginal utility of the last rand spent on each good? Show all your calculations.

Answer 1

Quantity of each good consumed

let X=5Y, and Z=4Y

$25Y+Y+16Y=37$

$42Y=37$

$Y=0.880952381$

quantity cannot be fraction so Y is approximately 1

$X=\frac{25\times 0.880952381}{5}=4.404761905$

Quantity cannot be a fraction therefore X is approximately 4

$Z=\frac{16\times 0.880952381}{4}=3.523809524$

quantity cannot be a fraction therefore Z is approximately 4

total consumption $= 5X+1Y+4Z=37$

total utility $=5+1+4=10$

marginal utility of X= 5

marginal utility of Y=1

marginal utility of Z=4