Intermediate Microeconomics Preferences Using the Slutsky Substitution

Intermediate Microeconomics Preferences

A consumer has a demand function for good 1:
x_1 (p_1,p_2,m)=19+m/(4p_1 )+6p_2
Where p_1 and p_2 are respective prices of good1 and good2 and m is the income.

I am halfway through my questions.

g) Assume well-behaved preferences and draw a diagram, with x_1 on the horizontal axis and x_2 on the vertical axis, showing the Slutsky substitution effect and income effect you calculated in parts d) through e). Label the initial budget line, the final budget line, and the line that passes through the initial bundle and is parallel to the final budget line, and show the axis intercepts for each. Show the coordinates of the optimal bundles on each budget line and draw the indifference curves through these optimal bundles. Show the substitution and income effects on both goods with arrows.

I need help with g and the following are the answers I had for d and e that are required for this problem:

D).

p1x1+p2x2=m
Original Price: 1x1 + 1x2 = 100
x1 = 19 + m = 100/4(1) + 6(1) = 50

Price decreases: 0.5x1 + 1x2 = 100
X1 = 19 + m =100/4(0.5) + 6(1) = 75

?m=x1?p1
=50 x (0.5-1)
= -25
Therefore,

m^'= m+ ?m
=100-25
= 75

Sub new values into the demand function;

x1(p^' 1,p2,m^' )= x1(0.5,1,75)
= 19 + 75/4(0.5) + 6(1)
= 62.50

Resulting in;

?xs1=x1(0.5,75)
=x1(1,1,100)
= 62.5 - 50
= 12.5

Therefore $12.50 is the price change effect caused by the Slutsky Substitution.

E).

x1(0.5,1,100)= 19+100/2+6
= 75

?x_1^I= x_1^F- x_1^I
= 75 - 62.5
= 12.5

I also need help with 2 more problems:

h) Using your diagram, for each good, determine whether it is an inferior good or normal good. Justify your answer. If there is not sufficient information to determine the type of good, explain why.

i) Using your diagram, for each good, determine whether it is an ordinary good or Giffen good. Justify your answer. If there is not sufficient information to determine the type of good, explain why.