Exam 5: The Theory of Demand

Suppose the consumer's utility function is given by $\mathrm { U } ( \mathrm { x } , \mathrm { y } ) = \mathrm { x } ^ { 1 / 4 } \mathrm { y } ^ { 3 / 4 }$ where $M U _ { x } = \frac { y ^ { \frac { 8 } { 4 } } } { 4 x ^ { \frac { 8 } { 4 } } } \quad M U _ { y } = \frac { 3 x ^ { \frac { 2 } { 4 } } } { 4 y ^ { \frac { 1 } { 4 } } }$ The equation for this consumer's demand curve for $x$ is:

Let $\mathrm { U } ( \mathrm { x } , \mathrm { y } ) = \sqrt { x y }$ with $\mathrm { MU } _ { \mathrm { x } } = \frac { \sqrt { y } } { 2 \sqrt { x } }$ and $\mathrm { MU } _ { \mathrm { y } } = \frac { \sqrt { x } } { 2 \sqrt { y } }$ . Let $\mathrm { I } = \$ 100 , \mathrm { P } _ { \mathrm { x } } = \$ 10$ and $\mathrm { P } _ { \mathrm { y } } = \$ 10$ be the initial set of prices and income. Now, let $P _ { x }$ rise to $\$ 25$ . What are the (approximate) substitution and income effects of this change in prices?

As the price of a good whose units are measured along the x-axis increases, holding the consumer's income and the price of the other good constant, the budget line will:

Assume that the price of good $x$ increases. The overall effect shows that the consumer purchases more of good $x$ if good $x$ is an inferior good.

Assume that the price of good $x$ increases. If x is an inferior good, the income effect alone leads to a decrease in consumption of good x.

If $x$ is a normal good and the price of $x$ falls:

The "substitution bias" of the CPI can be corrected partially by periodically updating the fixed basket of goods used in calculations.

Identify the statement that is true. Assume that the price of good $x$ increases.

In order to identify a consumer's demand curve from an optimal choice diagram we:

If $x$ is an inferior good and the price of $x$ falls:

Suppose when the consumer's income rises by 100%, the consumer's consumption of good $x$ only increases 1%. We can infer that good $x$ is a(n):

Let $\mathrm { U } ( \mathrm { x } , \mathrm { y } ) = \sqrt { x y }$ with $\mathrm { MU } _ { \mathrm { x } } = \frac { \sqrt { y } } { 2 \sqrt { x } }$ and $\mathrm { MU } _ { \mathrm { y } } = \frac { \sqrt { x } } { 2 \sqrt { y } }$ . Let $\mathrm { I } = \$ 100 , \mathrm { P } _ { \mathrm { x } } = \$ 25$ and $\mathrm { P } _ { \mathrm { y } } = \$ 10$ be the initial set of prices and income. Now, let $\mathrm { P } _ { \mathrm { x } }$ fall to $\$ 10$ . What is the approximate compensating variation for this change in prices?

Assume that the price of good $x$ increases. The substitution effect leads to a decrease in consumption of x only if x is an inferior good.

Leisure can be:

If $x$ is an inferior good and the price of $x$ rises:

The consumer's demand curve can be obtained analytically by solving which two equations?

A curve that represents the consumer's "willingness to pay" is the consumer's:

Giffen goods probably occur most frequently when the good in question is a:

Assume that the price of good $x$ increases. The substitution effect shows that the consumption of good $x$ falls, regardless of whether $x$ is a normal or inferior good.

The substitution effect graphically is always denoted: