Suppose That Bruce Cares Only About Barbecued Chicken (B) and Fish

question 4

Essay

Suppose that Bruce cares only about barbecued chicken (B) and fish (F). His utility function is U = B^0.4F^0.6. The price of barbecued chicken is $5, and the price of fish is $10. Bruce has a budget of $100.
a. What Lagrangian equation can be used to solve Bruce's utility maximization problem?
b. Derive the first-order conditions for the maximization problem.
c. What is the solution to Bruce's maximization problem?

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Definitions:

Internal Diseconomies

Increased per unit costs that occur when a firm or industry grows beyond a certain size, leading to inefficiencies.

External Diseconomies

Negative effects experienced by third parties or the general public due to the activities of a business or industry, not reflected in market costs.

Decreasing-Cost Industry

An industry where the cost per unit of output decreases as the scale of production increases is known as a decreasing-cost industry.

Long-Run Equilibrium

A state in which all factors of production and costs are variable, allowing for the adjustment of all inputs, leading to optimal allocation of resources in the market.