Question

In: Economics

a) sketch the price offer curve in (X1,X2 space) and the ordinary demand function in (X2...

a) sketch the price offer curve in (X1,X2 space) and the ordinary demand function in (X2 and P2 space) for the case of perfect substitute

x1= x1*(P1,P2,M)= 0 if p1>p2 or M/P1 if P1<P2

x2= X2*(P1,P2,M)= 0 if P1<p2 or M/P if P1>P2

b) what is the form of inverse demand function for product 2 in the case of perfect complements?

Expert Solution

a) Here we need to show the ordinary demand function in X2 and P2 space. So, lets assume that X2's own price changes with P1 and M being constant.

In case of substitutes, Utility function will be given as U (X1, X2) = X1 +X2

The given equations are as follows:

The price offer curve and the ordinary demand curve could be given as shown in the picture below:

When price of X2 is at P2 , P2 < P1, so X2 = M/P2.

When P2 changes to P2', P1 = P2', giving 0 < X2 < M/P2.

When P2 changes to P2'', P2'' > P1, giving X2 = 0.

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b)

In case of perfect complements, Utility function will be given as U (X1, X2) = min {X1, X2}

X1* (P1, P2, M) = X2* (P1, P2, M) =

With P1 and M fixed, higher P2 leads to smaller X1* and X2*.

The price offer curve and the ordinary demand funtion of X2 will be as in the picture below:

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Rahul Sunny answered 1 year ago

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