Question

Suppose a consumer has preferences given by U(X,Y) = MIN[2X,Y]. Suppose PX = 1 and PY = 2. Draw the Income Consumption Curve for this consumer for income values

• M = 100

• M = 200

• M = 300

To do this, carefully draw the budget constraints associated with each of the prices for good X, and indicate the bundle that the consumer chooses in each case. Also, be sure to label your graph accurately.

Answer 1

U = MIN[2X, Y]

Budget line: M = X.PX + Y.PY

M = X + 2Y

For a fixed-proportions utility function, utility is maximized when 2X = Y

Substituting in budget line,

M = X + 2 x 2X = X + 4X = 5X

X = M / 5

Y = 2X = 2M / 5

(i) When M = 100, X = 100/5 = 20, Y = 2 x 20 = 40

Budget line: 100 = X + 2Y

When X = 0, Y = 100/2 = 50 (Vertical intercept) & when Y = 0, X = 100 (Horizontal intercept).

In following graph, AB is the budget line when M = 100 with P being optimal (X, Y) bundle.

(ii) When M = 200, X = 200/5 = 40, Y = 2 x 40 = 80

Budget line: 200 = X + 2Y

When X = 0, Y = 200/2 = 100 (Vertical intercept) & when Y = 0, X = 200 (Horizontal intercept).

In above graph, CD is the budget line when M = 200 with Q being optimal (X, Y) bundle.

(iii) When M = 300, X = 300/5 = 60, Y = 2 x 60 = 120

Budget line: 300 = X + 2Y

When X = 0, Y = 300/2 = 150 (Vertical intercept) & when Y = 0, X = 300 (Horizontal intercept).

In above graph, EF is the budget line when M = 300 with R being optimal (X, Y) bundle.

Income consumption curve (ICC) is the line connecting the points P, Q and R.