For each of these utility functions write out the consumers

For each of these utility functions, write out the consumer\'s utility maximization problem in full, when the price of good x is 10, the price go good y is 20, and income is 500.

Solution

a)in this cobb douglas function

MRS=2y/4x

budget constraint=500=10x+20y

where price ratio is px/py

first rule of utility maximization yield

MRS=10/20

2x/4x=10/20

y=4x/2(10/20)x

substituting into budget constraint yields=

x*=(2/2+4)x500/10

y*=(4/2+4)x500/20

U=xy=(500/2x10)(500/2x20)

U=(500)^2/4X10X20