Answer to Question #190190 in Microeconomics for Tayyaba

Question

Suppose that the price of commodity Y is $1 per unit while the price of commodity X is $2 per unit and suppose that an individual’s money income is $16 per time period and is all spent on X and Y. (a) Draw the budget constraint line for this consumer and (b) explain the reason for the shape and the properties of the budget constraint line in part (a).

Answer 1

a) The equation of budget line or budget constraint is:

=(Price of good 1 × Quantity bought of good 1) +

 (Price of good 2 × Quantity bought of good 2) = Income

let commodity X be good 1 and let commodity Y be good 2. 

Price of commodity X = $2 per unit

Price of commodity Y =$1 per unit

Income= $1 per unit

Let the quantity bought of good X and good Y be X and Y. 

The budget constraint will be as follows:

$(\$2 \times X) + (\$1×Y)$

$2 X + Y = 16$

Thus, the budget constraint is given by:

2X + Y = 16. 

 To draw the budget constraint, we will need to find the intercept for each good, i.e., the maximum quantity that can be bought of each good from the income of the consumer. 

 The intercept is given by:

$Intercept \space of\space good = \frac{Income}{Price\space of \space good}$

Using the formula, we will find the intercept for both goods

$intercept of good X = \frac{16}{2}= 8$

$Intercept of good y =\frac{16}{1}= 16$

This implies that the consumer can purchase 8 units of good X and 16 units of good Y. 

 We take good X on the horizontal axis and good Y on the vertical axis and plot the points on the graph. The intercepts give us the points (8,0) and (0,16). 

The budget constraint is given by line AB. 

b) The budget constraint is downward sloping as the consumer has a limited income. To buy more of one good, he/she will need to reduce the consumption of the other good which makes it downward sloping. 

The budget constraint is a straight line which shows that the opportunity cost of consuming one more unit of good is the same for all the bundles. 

It is based on the income of the consumer as the constraint is due to limited income. 

When the consumer tries to maximize his/her utility, he/she will choose a combination where the budget line will be tangent to the indifference curve.