Question

For each of the following utility functions, explain whether the preferences that they represent are strictly convex. Use indifference curve diagrams to help explain your answers.

1. Preferences represented by u (x1, x2) = x1 + x2.

2. Preferences, represented by u (x1, x2) = min {x1, x2}.

Answer 1

Answer 1 :-

This is the case of perfect substitute which represents straight line Indifference curves. Two goods are said to be perfect substitutes when the marginal rate of substitution of one giodfor the other is constant There are straight lines and tangency is not possible. The equilibrium position will depend on the slope of the priceline relative to the slope of indifference curve. If the slope of the price line is Greater and touches the highest indifference curve on y axis then the consumer will choose to buy good b only .However if the slope of the price line is lower and touches the highest indifference curve on x-axis then the consumer will only chooseto buy Good A . IC1 represents lowest Indifference utility value and this value keeps on increasing as a consumer moves to higher Indifference curves.

Answer 2 :-

This is the case of perfect complement goods. Here the Indifference curves are right angled. In such a case a consumer's equilibrium will be at the corner of the curve where the price line is tangent. Ic1 represents the indifference curve with the lowest utility and as a consumer moves to higher Indifference curves it derives higher level of utility