Question

Suppose that a typical consumer’s utility function is characterized by the following relation between good X and good Y. The consumer’s consumption decision is influence by the price of the respective goods, which requires him 2 birr for each unit of X and 3 birr for each unit of Y and the resource available to him is 160 birr.
A construct the budget constraint of this typical consumer(2pts)
Find the optimal consumption of X and Y(5pts)

Answer 1

a)

According to question resource available to the consumer is 160 birr .

Taking birr as the currency unit .

Income = 160 birr 

Price of commodity X = 2 birr

Price of commodity Y = 3 birr 

Income spent on Commodity X = 2X 

Income spent on Commodity Y = 3Y 

Budget Constraint : Total Expenditure </= Total Income 

Expenditure on Commodity X + Expenditure on Commodity Y </= Total Income 

Putting in Values we get :

Budget Constraint :  $2X + 3Y </= 160$

 b)

Now , optimal bundle for a consumer is achieved where the slope of budget constraint and slope of the indifference curve is equal .

Slope of IC curve = - MRS (Marginal Rate of Substitution)

Slope of Budget Constraint $\frac{y2 - y1}{ x2 - x1 }= \frac{\frac{I}{3}-0}{\frac{I}{2}-0}$

$= - \frac{2}{3}$

Negative signs are used as the slopes are decreasing in nature

Point A is the optimum bundle . As at point A .

$-MRS = - \frac{2}{3}$