Example: A consumer has $100 to spend on two goods X and Y with prices $3 and $5 respectively. Derive the equation of the budget line and sketch the graph.

Answer 1

To derive the equation of the budget line, we first need to determine the quantity of goods X and Y that the consumer can afford with their $100 budget.

Let's assume the consumer can purchase x units of good X and y units of good Y.

The total cost of good X will be the price of X multiplied by the quantity of X: Cost of X = $3x.
The total cost of good Y will be the price of Y multiplied by the quantity of Y: Cost of Y = $5y.

Since the consumer has a budget of $100, we can set up the following equation:

Cost of X + Cost of Y = Total Budget.
$3x + $5y = $100.

Now, we can rearrange the equation to solve for y in terms of x:

$5y = $100 - $3x
y = (100 - 3x) / 5.

This is the equation of the budget line. It represents all the combinations of goods X and Y that the consumer can afford with their $100 budget.

To sketch the graph, we can plot several points on the X-Y plane to represent different combinations of goods X and Y that the consumer can purchase.

Let's choose some values for x and plug them into the equation to find the corresponding y values:

When x = 0, y = (100 - 3(0)) / 5 = 100 / 5 = 20.
When x = 10, y = (100 - 3(10)) / 5 = 70 / 5 = 14.
When x = 20, y = (100 - 3(20)) / 5 = 40 / 5 = 8.

Now we can plot these points on the graph and draw a line passing through them to represent the budget line.