Answer to Question #279671 in Microeconomics for Shashi

Question

mux=120-10x

muy=160-20y

price of x=rs.10/=

price of y= rs.20/=

income=220/=

calculate the total utility from the consumption of 4 units of good x and 5 units of good "y

Answer 1

Total utility is found by integrating the marginal utilities for both x and y and summing them.

Therefore the total utility function will be as below:

$U(x,y)=(120x-5x^{2})+(160y-10y^{2})$

The consumers budget line from the information can be summerized as

$10x+20y=220$

When the consumer consumes 4 units of good x and 5 units of good y, he spends a total of rs.140.

The utility derived from such a combination will be:

$U(x,y)=(120\times 4-5\times 4^{2})+(160\times 5-10\times 5^{2})$

$U(x,y)=400+550$

$U(x,y)=950$