Question

7) a) What is the relationship between marginal rate of substitution (MRS) and the concept of an indifference curve? b) Suppose a consumer's utility function is defined by u(x,y)=3x+y for every x>0 and y0. Calculate a formula for MRS at every combination of x and y. c) Suppose that P,-/ P, and that this consumer has an initial endowment of wealth w=100. Find this individual's utility maximizing demand of x and y. 10 pts

Answer 1

a) the slope of indifference curve is given by MRS which is the rate at which consumer is willing to substitute x for y.
b) U = 3x + y

MUx= dU/dx = 3

MUy= dU/dy = 1

MRS = 3/1= 3

c) Px/Py= 1/1= 1

x and y are substitutes, so only one will be consumed.

Because MRS is greater than Px/Py, only x will be consumed.

x= 100/1= 100
y= 0

Answer 2

The Marginal Rate of Substitution (MRS) is intimately tied to the concept of indifference curves in microeconomics. An indifference curve is a graphical representation showcasing combinations of two goods that yield the same level of satisfaction for a consumer. The MRS, depicted by the slope of the indifference curve at any point, quantifies the rate at which a consumer is willing to trade one good for another while maintaining constant satisfaction. This ratio, expressed as the marginal utility of one good divided by the marginal utility of another, exemplifies the diminishing nature of consumer preferences. As one moves along an indifference curve, indicating different combinations of goods, the MRS diminishes, illustrating the principle of diminishing marginal utility. The equilibrium point, where the budget constraint is tangent to the indifference curve, signifies the consumer's optimal allocation of resources, ensuring that the ratio of prices equals the MRS, and adheres to the principle of equimarginal utility. Thus, the relationship between MRS and indifference curves is fundamental in understanding how consumers make choices based on their preferences and budget constraints.