Suppose a consumer, Sheldon Cooper,

Suppose a consumer, Sheldon Cooper,

Suppose a consumer, Sheldon Cooper, has the following utility function for comic books (C) , and tangerine chicken (T):( See Image for Utility function )..Use the utility function to define the indifference curve that passes through all of the bundles of C and T that provide the consumer with exactly 10 units of utility and solve the indifference curve for T as a function of C. (Hint: set the utility function equal to 10) Find the marginal rate of substitution as a function of C (for just the indifference curve in part (a)) by differentiating the indifference curve with respect to C; is the indifference curve downward sloping? Does the indifference curve have a diminishing marginal rate of substitution? Prove using calculus or with a numerical example, and remember that we’re concerned with how the absolute value of the MRS changes. Find the marginal rate of substitution as a function of both C and T by using the definition involving marginal utilities. (This is the more general representation of MRS as it applies to all possible bundles and so to the complete set of ICs.)

 

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