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University of California, San Diego  ECON 100A 1)Matt gets utility from apples and bananas and his preferences can be represented by the utility function U(A,B)=A+4B

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University of California, San Diego  ECON 100A

1)Matt gets utility from apples and bananas and his preferences can be represented by the utility function U(A,B)=A+4B.  If the price of apples is 2 times the price of bananas, what is Matt's ordinary demand function for apples, A(p_A, p_B, I)?

2. David gets utility from X and Y and his preferences can be represented by the utility function  U(x,y)=min{X, 1/3Y}.  David maximizes his utility subject to a budget constraint.  What is his Marshallian demand function for Y i.e., Y(p_X, p_Y, I)? 

Use the facts that 

1. 1. solution will be at a kink point, with no excess Y or X, so X=1/3Y 
   2. utility maximizing bundle must be on the budget constraint (PxX+ PyY =I). 

3. Toni’s utility over x₁and x₂ can be represented by the utility function, U(x₁, x₂)= x₁²+ x₂².  If the price of x₁ is $10 and the price of x₂ is $25 and Toni has $200 to spend, what commodity bundle will maximize Toni’s utility given her budget constraint?  

4. Briana's utility over X and Y can be represented by U(X,Y)=2X-lnY.  Briana maximizes her utility subject to a budget constraint.  What are her uncompensated demand functions, X*(p_X , p_Y, I) and Y*(p_X, p_Y, I)?  

5. TRUE or FALSE or Uncertain:  Can a consumer ever be maximizing her utility subject to her budget constraint if the "bang-for-her-buck" (her added utility from the last dollar spent on the good) is not the same across all of the goods she consumes?