Question

Burt’s utility function is U(x1, x2)= min{x1,x2}. Suppose the price of good 1 is p1, the price of good p2, the income is y.
a. Derive ordinary demand functions.
b. Draw indifference curves and budget line for the case when the price of good 1 is 10, the price of good 2 is 20, the income is 1200.
c. Find the optimal consumption bundle.

Answer 1

The utility function of the consumer is given as:

U= min (x1, x2)

Lt the budget function be:

M= p1x1 +p2x2

The utility function is of perfect complements, the consumer's utility will be maximum, when it consumes the complements in the proportion as he wants.

in the case of this w=utility function, the consumers, utility will be maximum when he consumes x1 and x2 in the ratio of 1:1

Thus, his utility will be maximum when

x1= x2The optimizaton condition becomes

x1/ x2= p1/p2

p1= p2 [ As x1= x2]

Putting the value of x1= x2 and p1=p2 in the budget constraint;

M= p1x1 +p1x1

X1= M/2p1

This is the demand function for x1

In a similar way we will get the demand fucntion for x2 as

x2= M/2p2

b) It is given that M= 1200, P1= 10, p2= 20

The horizontal intercept will be M/p1= 1200/10= 120

The vertical intercept will be M/ p2= 1200/ 20= 60

The indifference curve will be L shaped as the utility function represents the utility of perfect complements.

Diagramatically it can be shown as: