Question

Q1) Haroon’s budget line relating good X and good Y has intercept of 100 unit of good X and 40 units of good Y. if the price of good X is 24, what is Haroon’s income? What is the price of good Y? What is then slope of budget line?

Answer 1

The budget line will take the form of:

$$M = xP_x + yP_y$$

Solving for $y$ in the budget line:

$$y = \dfrac{M}{P_y} - \dfrac{P_x}{P_y} x$$

Where:

• M is the income
• $P_y$ is the price of good Y and,
• $P_x$ is the price of good X.

Here, the slope of the budget line is $-\dfrac{P_x}{P_y}$

At the y-intercept, the value of good X consumed is zero. Therefore:

$$M = yP_y$$

Solving for ''y'', we get:

$$y = \dfrac{M}{P_y}$$

At the y-intercept, y = 40. Therefore:

$$40 = \dfrac{M}{P_y}$$

Solving for $P_y$ :

$$P_y = \dfrac{M}{40}$$

At the x-intercept, the amount of Y consumed is zero. Therefore:

$$M = xP_x$$

Solving for ''x'':

$$x = \dfrac{M}{P_x }$$

The x-intercept is 100. Therefore:

$$100 = \dfrac{M}{P_x }$$

Solving for $P_x$ :

$$P_x = \dfrac{M}{100}$$

Therefore, the slope is:

$$-\dfrac{P_x}{P_y} = -\dfrac{\dfrac{M}{100}}{\dfrac{M}{40}}$$

$$-\dfrac{P_x}{P_y} = -\dfrac{M}{100}\times \dfrac{40}{M}$$

$$-\dfrac{P_x}{P_y} = \color{red}{-0.4}$$