Calculus-Based MRS Calculation at Point A

An individual's preferences for daily hours of free time (t) and consumption (c) are represented by the utility function u(t, c) = (t-6)²(c-45). At a point where the individual has 16 hours of free time and a consumption level of 95, what is the value of their marginal rate of substitution (the rate at which they are willing to trade consumption for an additional hour of free time)?

Deriving the Marginal Rate of Substitution Formula

Analyzing a Flawed MRS Calculation

Consider an individual whose preferences for daily hours of free time (t) and consumption (c) are represented by the utility function u(t, c) = (t-6)²(c-45). True or False: According to this model, the more free time this individual has, the less consumption they are willing to sacrifice for an additional hour of free time, assuming their consumption level is held constant.

An individual's preferences for daily hours of free time (t) and consumption (c) are represented by the utility function u(t, c) = (t-6)²(c-45). Match each economic concept below to its correct mathematical representation based on this utility function.

Applying the Marginal Rate of Substitution

To derive the Marginal Rate of Substitution (MRS) from the utility function u(t, c) = (t-6)²(c-45), where 't' is free time and 'c' is consumption, a specific sequence of calculus-based steps must be followed. Arrange the following steps in the correct logical order.

For an individual whose preferences for daily hours of free time (t) and consumption (c) are represented by the utility function u(t, c) = (t-6)²(c-45), their marginal rate of substitution is given by the formula 2(c-45) / (____).

Evaluating a Work-Life Trade-off

Analyzing Preferences from a Utility Function

Consider an individual whose preferences for daily hours of free time (t) and consumption (c) are represented by the utility function u(t, c) = (t-6)²(c-45). True or False: According to this model, the more free time this individual has, the less consumption they are willing to sacrifice for an additional hour of free time, assuming their consumption level is held constant.