The price of good X is $50. a) What is the consumer's income on budget line B_1? b) What is the...

a)

The consumer's income on budget line B1 is calculated below:

{eq}\begin{align*} {P_X} &= \$ 50\\ Income &= 50 \times 80\\ &= 4000 \end{align*} {/eq}

The income of the consumer will be $4000.

b)

The price of good Y on Budget line B1 is calculated below:

{eq}\begin{align*} {P_Y} &= \dfrac{{4000}}{{40}}\\ &= 100 \end{align*} {/eq}

The price of good Y will be $100.

c)

The equation of the budget line B1 is calculated below:

{eq}\begin{align*} {P_X} &= \$ 50\\ {P_Y} &= \$ 100\\ M &= 4000\\ {P_X}X + {P_Y}Y &= M\\ 50X + 100Y &= 4000 \end{align*} {/eq}

d)

The consumer's marginal rate of substitution when she is at equilibrium at point A is calculated below:

{eq}\begin{align*} MR{S_{XY}} &= \dfrac{{{P_X}}}{{{P_Y}}}\\ &= \dfrac{{50}}{{100}}\\ &= \dfrac{1}{2} \end{align*} {/eq}

e)

The prices of X and Y on budget line B2 are calculated below:

{eq}\begin{align*} M &= 4000\\ X &= 100\\ Y &= 40\\ {P_X}X + {P_Y}Y &= M\\ 100{P_X} + 40{P_Y} &= 4000\\ {P_X} &= \dfrac{{4000}}{{100}}\\ &= 40\\ {P_Y} &= \dfrac{{4000}}{{40}}\\ &= 100 \end{align*} {/eq}

The price of good X will be $40, and good Y will be $100.

f)

The prices of X and Y on budget line B3 are calculated below:

{eq}\begin{align*} M &= 4000\\ X &= 100\\ Y &= 50\\ {P_X}X + {P_Y}Y &= M\\ 100{P_X} + 50{P_Y} &= 4000\\ {P_X} &= \dfrac{{4000}}{{100}}\\ &= 40\\ {P_Y} &= \dfrac{{4000}}{{50}}\\ &= 80 \end{align*} {/eq}

The price of good X will be $40, and good Y will be $80.

g)

The income level at B3 is calculated below:

{eq}\begin{align*} X &= 100\\ {P_X} &= 50\\ Income &= X \times {P_X}\\ &= 100 \times 50\\ &= 5000 \end{align*} {/eq}

The income level will be $5000.