Kelly’s utility function is given by U = 5X + 2Y, where MUX = 5 and MUY = 2
I know MRSxy would be 2.5
What is MRSXY when X = 1 and Y = 5? When X = 2 and Y = 2.5?
Also how would I draw a sample indifference curve?
To find the Marginal Rate of Substitution (MRS) between X and Y in Kelly's utility function, you can calculate the ratio of the marginal utilities of X and Y.
MRSXY = MUX / MUY
Given that MUX = 5 and MUY = 2, the MRSXY is:
MRSXY = 5 / 2 = 2.5
When X = 1 and Y = 5, the MRSXY remains the same:
MRSXY = MUX / MUY = 5 / 2 = 2.5
Similarly, when X = 2 and Y = 2.5, the MRSXY remains the same:
MRSXY = MUX / MUY = 5 / 2 = 2.5
As for drawing a sample indifference curve, follow these steps:
1. Identify the utility level: Choose a specific utility level, such as U = 10, 15, or any other value you prefer.
2. Determine the possible combinations of X and Y that yield the chosen utility level: Rearrange the utility function to solve for Y in terms of X, using the chosen utility level. For example, if U = 10, the equation becomes Y = (10 - 5X) / 2.
3. Choose different values of X: Select different values for X and calculate the corresponding values of Y using the equation from step 2.
4. Plot the points: Plot the values of X and Y on a graph.
5. Connect the points: Draw a smooth curve that passes through the plotted points. This curve represents the indifference curve, as it represents combinations of X and Y that give the same level of utility.
6. Repeat: You can repeat this process for different utility levels to draw multiple indifference curves.
Keep in mind that the exact shape of the indifference curve depends on the specific utility function and the preferences of the individual.