Sure. The budget like I will reference in the methods below is as follows: p1*x1 + p2*x2 = w. Method 1: Write the budget line in slope-intercept form by solving for x2 as a function of x1: x2 = - (p1/p2)*x1 + w/p2 Recall that slope-intercept form for y as a function of x is: y = a*x + b, where a is the slope and b is the intercept. Therefore, the slope of the budget like is -p1/p2. Method 2: Write the budget line as a function F(x1,x2) = 0 and use the Implicit Function Theorem: F(x1,x2) = p1*x1 + p2*x2 - w Now use the Implicit Function Theorem to find the slope dx2/dx1: dx2/dx1 = -(dF/dx1)/(dF/dx2) = -p1/p2 If you're not familiar with the Implicit Function Theorem, I would recommend just sticking with Method 1.
Hi, could you please show how you did the derivatives part to find the slope of the line -p1/p2
Sure. The budget like I will reference in the methods below is as follows: p1*x1 + p2*x2 = w.
Method 1: Write the budget line in slope-intercept form by solving for x2 as a function of x1:
x2 = - (p1/p2)*x1 + w/p2
Recall that slope-intercept form for y as a function of x is:
y = a*x + b,
where a is the slope and b is the intercept. Therefore, the slope of the budget like is -p1/p2.
Method 2: Write the budget line as a function F(x1,x2) = 0 and use the Implicit Function Theorem:
F(x1,x2) = p1*x1 + p2*x2 - w
Now use the Implicit Function Theorem to find the slope dx2/dx1:
dx2/dx1 = -(dF/dx1)/(dF/dx2) = -p1/p2
If you're not familiar with the Implicit Function Theorem, I would recommend just sticking with Method 1.
Quality and it will take care of my favorite