The Preferences for Californians Can Be Represented by the Following

question 28

Essay

The preferences for Californians can be represented by the following utility function:
U(X,Y)= X^aY^1-a.The consumer faces the budget constraint I = p.X + q.Y,where I is the agent's income,and p and q are the prices.Suppose the government imposes a consumption restriction so that any person in the state is allowed to consume 50 units of electricity at most.
a.If a = 0.25,I = 100,and both prices are equal to one,find the optimal consumption of gasoline and electricity by the agent.Is the electricity constraint binding? (Hint: solve the problem without the 50 ≥ X constraint and see if the solution satisfies the constraint.If your answer then does not satisfy 50 ≥ X,the solution must be 50 = X)
b.How does your answer in part a.change if a = 0.75? Explain.
c.On a graph,illustrate the answers to parts a.and b.

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Definitions:

Revenues

The overall income earned from transactions of goods or services central to a business's core functions.

Operating Revenues

The income earned from a company's main business operations, excluding income from investments or secondary sources.

Operating Expenses

The costs associated with the normal operations of a business, excluding costs related to producing goods or services, like rent, utilities, and salaries.

Interest Expense

The cost incurred by a company for borrowed funds, shown as an expense on the income statement.