00:01
So to derive the consumer's ordinary demand function, we need to find the optimal values of x and y that maximize the consumer's utility subject to her budget constraint.
00:12
The consumer's utility function is u of x, y equals x.
00:23
And her budget constraint can be expressed as p times x is multiplied plus a p2 times y equals m.
00:45
Where p is the price of good x, p2 is the price of good y, and m is the consumer's income.
00:54
So to find the ordinary demand function for good x, we will maximize the utility function u of x, y equals x with respect to x subject to the budget constraint.
01:06
So step one, maximize utility.
01:16
So we need to maximize u of x, y equals x subject to the budget constraint p times x plus p2 times y equals m.
01:27
Next, we need to formulate the lagrangian function.
01:32
So the lagrangian function or l is defined as l of x, y, lambda equals x minus lambda times p times x plus p2 times y minus m, where lambda is the lagrange multiplier.
02:16
Step three, we need to take partial derivatives.
02:24
Partial and set equal to zero.
02:36
So when we do l over x equals one minus lambda times p equals zero, then we have l over x equals zero.
03:08
And then we have l over x equals p times x plus p2 y minus m equals zero...