Question

A consumer's preference over beer (x) and wine (y) is such that he is indifferent between drinking 3 beers and 5 wines.

The price of x is 414, the price of y is 682. The consumer's income is 10,500. What is her optimal consumption of product y?

Answer 1

A consumer's preference over beer (x) and wine (y) is such that he is indifferent between drinking 3 beers and 5 wines.

U = 3x + 5Yy

Px (Price of x) = 414

Py (Price of y) = 682

M (consumer income) = 10500

In case of substitute goods,

If (MUx / Px) > (MUy / Py) => Consumer will consume only good X

If (MUx / Px) < (MUy / Py) => Consumer will consume only good Y

MUx = ΔU / Δx

=> MUx = 3

MUy = ΔU / Δy

=> MUy = 5

(MUx / Px) = (3 / 414) = 0.007299

(MUy / Py) = (5 / 682) = 0.007331

Since,  (MUx / Px) < (MUy / Py) => Consumer will consume only good Y.

All the income would spend on the good y (i.e., wine)

=> Optimal consumption of Good Y = (M / Py)

=> Optimal consumption of Good Y = (10500 / 682)

=> Optimal consumption of Good Y = 15.39