Exam 9: Demand for Goods and Supply of Labor and Capital

Leisure being an inferior good is necessary but not sufficient for labor supply to slope up.

If a good is quasilinear,its own-price demand curve is vertical.

Suppose your utility function is given by $u \left( x _ { 1 } , x _ { 2 } \right) = \min \left\{ 3 x _ { 1 } , 5 x _ { 2 } \right\}$ .What is your demand function for $x _ { 2 }$ ?

Leisure being a normal good is neither necessary nor sufficient for labor supply to slope up.

A downward sloping income-demand curve indicates that the good is a necessity.

If future consumption is a normal good,the interest rate/borrowing relationship cannot be upward sloping.

If tastes are homothetic in leisure and consumption,labor supply curves slope up.

The empirically observed backward-bending labor supply curve cannot arise from homothetic tastes.

Suppose your tastes can be represented by the utility function $u \left( x _ { 1 } , x _ { 2 } \right) = x _ { 1 } ^ { 2 } + x _ { 2 } ^ { 2 }$ .Your demand for $x _ { 1 }$ is a. $\frac { I } { 2 p _ { 1 } }$ . d. $\frac { I } { p _ { 1 } }$ if $p _ { 1 } < p _ { 2 }$ and 0 if $p _ { 2 } < p _ { 1 }$ . b. $\frac { p _ { 1 } I } { p _ { 1 } ^ { 2 } + p _ { 2 } ^ { 2 } }$ . e. None of the above c. $\frac { I } { p _ { 1 } + p _ { 2 } }$ .

In order for someone to switch from borrowing to saving when the interest rate falls,it must be that current consumption is an inferior good.

The cross-price demand curve for Cobb-Douglas tastes is perfectly vertical.

Suppose your tastes over consumption and leisure have constant elasticity of substitution.I observe that,when your wage went up,you continued to work the same number of hours.From this,I can conclude that you have Cobb-Douglas tastes.

An increase in the price of good 2 will cause the demand curve for good 1 to shift out.

Goods like exclusive designer clothes carry with them prestige value linked to their price.As a result,some people demand more of such goods as the price increases.For those people,such goods are Giffen goods.

Assuming the same sized substitution effect,normal goods have steeper cross-price demand curves than inferior goods.

Consider a consumer who consumes only $x _ { 1 }$ and $x _ { 2 }$ .The price of $x _ { 2 }$ falls. a.On a graph with $x _ { 1 }$ on the horizontal and $x _ { 2 }$ on the vertical axis,illustrate the change in this consumer's budget constraint assuming exogenous income I. b.Illustrate income and substitution effects for $x _ { 1 }$ assuming that both goods are normal. c.Can you tell whether the cross-price demand curve for $x _ { 1 }$ is upward or downward sloping? d.Suppose $x _ { 1 }$ is leisure hours and $x _ { 2 }$ is a composite consumption good.Consider an increase in the wage assuming a fixed endowment of leisure (and no exogenous source of income).How is your graph similar and how is it different from what you graphed in (a)through (c)? e.Is the leisure-demand curve a cross-price demand curve? Why or why not?

For the same sized substitution effect,own-price demand curves for inferior goods are steeper than own price demand curves for normal goods.

Since income and substitution effects point in the same direction for normal goods,the leisure demand curve will be shallower if leisure is a normal good than if leisure is an inferior good.

Unless a good is a Giffen good,the demand curve shifts to the right as income rises.

Suppose that utility over consumption and leisure takes the constant elasticity of substitution form $u ( \ell , c ) = \left( \alpha \ell ^ { - \rho } + ( 1 - \alpha ) c ^ { - \rho } \right) ^ { - 1 / \rho }$ .If $\rho$ falls between 0 and -1,then the labor supply curve is backward bending.