Question

Determine whether or not the following statements are true or false.

A. If the income consumption curve is vertical, the Engel curve for good y is upward sloping.

B. If the price consumption curve (as the price of good x changes) is vertical, the price elasticity of demand for good x is zero.

C. An upward sloping price consumption curve (as the price of good x changes) indicates that goods x and y are complements in consumption.

D. If preferences over goods x and y are represented by U(x,y) = 3x^1/2 y^1/2 , the price consumption curve (as the price of x changes) is necessarily horizontal.

E. If U(x,y)= 3 + ln(x) + 5y, the income consumption curve is vertical, assuming an interior solution.

Answer 1

a. True. When the income-consumption curve is vertical means with the rise in the income of the consumer, the demand of the good x is not changing or increasing but is constant while the demand for good y is rising. So when we draw the engel curve with income on horizontal axis, and demand on vertical axis, it would be upward sloping for good y, but parallel to horizontal axis for good x.

b.True, the vertical price consumption curve means that the demand is not rising with the fall in the price. So the price elasticity which actually measures the degree of change in quantity demanded due to change in price would be zero.

c. Yes, because with the increase in the price of one good, the consumer must shift to the consumption of good 2. But here since both are rising or changing means that consumer must prefer both the goods at the same time meaning that both must be complements.

d. If we find the MRS of x for y in this part, it will be equal to 1. This implies that the goods are perfect substitutes. When the goods are perfect substitutes, then with the decline in the price of one good will make consumer switch to other good. In case of perfect complements, the PCC will be horizontal but same as x-axis.