Suppose That Ken Cares Only About Bathing Suits (B) and Flip-Flops

question 61

Essay

Suppose that Ken cares only about bathing suits (B) and flip-flops (F). His utility function is U = B^0.8F^0.2. The price of bathing suits is $30, and the price of flip-flops is $2. Ken has a budget of $150.
a. What Lagrangian equation can be used to solve Ken's utility maximization problem?
b. Derive the first-order conditions for the maximization problem.
c. What is the solution to Ken's maximization problem?

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Definitions:

Autotrophs

Organisms that produce their own food from inorganic substances using light or chemical energy, such as plants and algae.

Energy Flow

Energy flow describes the movement of energy through an ecosystem, from primary producers through various consumers, and ultimately to decomposers.

Ecosystem

An ecological community comprising both living organisms and their physical surroundings that interact with each other.

Physical Environment

refers to all the physical and abiotic factors that surround and affect the survival and development of organisms, such as water, air, temperature, and geography.