Answer to Question #263700 in Microeconomics for Star

Question

Billy Madison consumes 100 units of X and 50 units of Y. The price of x rises from 2 to 3. The price of Y remains at 4.

a/ how much must Billy’s income rise so that he can exactly afford 100 units of x and 50 units of y?

b/ Draw Billy’s original budget set when the price of X is 2

c/ Draw Billy’s budget set when the price of X is 3, but his income is unchanged

d/ Draw Billy’s budget set when the price of X is 3 and his income increases by the amount in (a) so that he can afford his original consumption bundle.

Answer 1

a.

$income=p_xx+p_yy\\x=100,y=50\\p_x=2,p_y=4\\income=2(100)+4(50)=400$

now px rises to 3 , but x=100,y=50

$income=3(100)+4(50)=500\\$

income must rise by $=500-400=100$

b and c

original budget $400=2x+4y$

x intercept $=\frac{400}{2}=200$

y intercept $=\frac{400}{4}=100$

new budget $400=3x+4y$

x intercept $=\frac{400}{3}=133.33$

y intercept $=\frac{400}{4}=100$

d.

new budget $500=3x+4y$

x intercept $=\frac{500}{3}=166.67$

y intercept $=\frac{500}{4}=125$