The Preferences for Californians Can Be Represented by the Following

Essay

The preferences for Californians can be represented by the following utility function: U(X,Y)= XᵃY¹⁻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.