Question

1. Consumer’s utility function is: U (X,Y) = 10X + Y. Consumer’s income M is 40 euros, the price per unit of good X (i.e. Px ) is 5 euros and the price per unit of good Y (i.e. Py) is 1 euro.

a) What is the marginal utility of good X (MUx) for the consumer?

b) What is the marginal utility of good Y (MUy) for the consumer?

How do I calculate these?

Answer 1

The consumer utility is . All the other variables corresponds to budget constraint and are not necessary for MU's calculation.

MU is amount of utility that increase/decrease by consuming one more unit of the good. The MRS (marginal rate of substitution) is the slope of the utility function, and relates both MU's.

The easiest method of calculating the marginal utility is by partial differentiation of the utility function, ie and . It might seem too much here, but is very helpfull incase the utility fuction has powers of x or/and y greater than 1.

(a) or or or or .

(b) or or or or .

The basics of partial differentiation is to treat all other variable constant except the variable with respect to which we are differentiating.

BONUS (Spoilers/Answer ahead): The MRS in this case is , which is slope of line , as utility is taken constant to find the slope.

It can also be found by formula .

The budget line is , ie , and its slope is . This slope mis-match with the slope of MRS, and is hence, indicating a corner slotion. The graph is as below.

The indifference curve are drawn as IC4>IC3>IC2>IC1, ie the IC to right is more preferable than IC to left, since as utility in increases, the IC's shift right. The IC4 provides most utility that touches the Budget line at (x=8,y=0).