1. The utility function is given by:
and the budget line is
Then the price of good x goes up to 4.
Find the Hicksian substitution effect, income effect, and total change in demand for good x from the change
Ok i read the theory but i cant solve the problem at all. I just need to a little and maybe i can apply the theory into it. Any help would be appreciated.
I can see why you are confused. Your marginal rate of substitution in utility is constant, and therefore linear. Which means you will always have a corner solution. That is, the slope of any and all indifference curves is -1.
The slope of the initial budget constraint is -1/2, and the person consumes x only. With the price increase, the slope of the budget constraint becomes -2 and the person consumes all y.
With this, you should be able to calculate the hicksian substitution effect and the income effect. (Hint, its all substitution).