Question

Mike uses his 100 cent income to buy only coffee(x) and beer(y) only. Mike is characterized by utility maximization and saving no amount of money.

utility function : U = xy income consumption curve : y = 2x

1. If coffee's price is 10 cent calculate beer's price.

2. Calculate Mike's beer consumption amount.

Answer 1

From the utility function |MRS| = y/x and price ratio is Px/Py = 0.10/Py. At the optimal bundle |MRS| = Px/Py

y/x = 0.10/Py

From ICC, we see that y = 2x or y/x = 2. Use this in optimal bundle rule

2 = 0.10/Py

Py = 0.05 or 5 cents.

Price of beer is 5 cents

Consumption of beer is found using budget line

M = xPx + yPy

100 = x*10 + y*5

100 = 10x + 5y

100 = 10x + 5*2x

x* = 100/20 = 5 units

y* = 2x = 5*2 = 10 units. Hence Mike's beer consumption amount is 10 units.