Question

Henry’s utility function is U(x, w)= x²+ 16xw + 64x², where x is his consumption of good x and w is his consumption of good w.

	a.	Henry’s preference are nonconvex.
	b.	Henry’s indifference curves are straight lines.
	c.	Henry has a bliss point.
	d.	Henry’s indifference curves are hyperbolas.
	e.	None of the above.

Answer 1

Here, option (b) is the right answer. ie; for the above utility function U(x,w) = x2 +16xw + 64w2, the indifference curve would be straight lines

· An indifference curve connects the points on graphs representing different quantities of two goods, ie; it has the locus of two points showing different combinations of the two goods providing equal utility to a customer.

· An indifference curve is a straight line when the goods are better substitutes of each other.

· A downward sloping indifference curve indicates that the amount of one good in the combination is increased and the other is decreased.

The reason why it tends to a straight line can be given as follows.

· The above equation is x2 + 16xw + 64w2 which can be written as (x+8w)2

· Let (x+8w)2 = k

· Solving for k, (x+8w) = k1/2

                                X = k1/2 -8w

· Plotting x on the ‘y’ axis and w on the ‘x’ axis, the equation has a constant slope of -8. Hence, the given curves must be straight lines.

· Here option (a) is wrong in the sense that indifference curve are normally convex to the origin.ie; it is relatively flatter in the right hand portion and steeper towards the left hand portion. A diminishing marginal rate of substitution holds only for convex curves.

· In option (c ), as it is known, the indifference curves cannot intersect each other and hence a bliss point is not achievable. Hence option (c ) is also wrong.