Final answer:
To find the Marginal Rate of Substitution (MRS), we need to find the slope of the indifference curve. The indifference curve represents the combinations of goods that give the same level of utility to the consumer. In this case, the MRS is 2 and the graph can be plotted with X on the x-axis and Y on the y-axis with the given bundle and the indifference curve.
Step-by-step explanation:
To find the Marginal Rate of Substitution (MRS), we need to find the slope of the indifference curve. The indifference curve represents the combinations of goods that give the same level of utility to the consumer. In this case, the consumer's utility function is given by U(X,Y) = 4X + 2Y. Let's substitute X = 1 and Y = 3 into the utility function to find the utility level at this bundle.
U(1, 3) = 4(1) + 2(3) = 4 + 6 = 10.
The slope of the indifference curve is equal to the ratio of the marginal utility of good X (MUx) to the marginal utility of good Y (MUy). Let's calculate these values using the utility function.
MUx = ∂U/∂X = 4.
MUy = ∂U/∂Y = 2.
Now we can calculate the MRS:
MRS = MUx / MUy = 4 / 2 = 2.
The MRS represents the rate at which the consumer is willing to substitute good X for good Y while maintaining the same level of utility. In this case, the consumer is willing to give up 2 units of good Y to get 1 more unit of good X.
To draw the graph, we can plot different combinations of X and Y on a graph with X on the x-axis and Y on the y-axis. We will plot the given bundle X = 1 and Y = 3. We can also plot the indifference curve that represents the combinations of goods that give the same level of utility. Each point on the indifference curve represents a different combination of X and Y that gives the consumer the same level of utility.