Suppose you have follow ing utility function : UX1,X2)-Xx2 where 0<0<1; 0<B< 1; 0<B+0<1 The price...
Suppose you have following utility function :U(x,y)=(x + yaja where x >0, y>0 and a 70, a <1 The price of commodity x is P >0 and the price of good y is P, > 0. Let us denote income by M, with M>0 a) Compute the marginal utilities of X and Y. b) Write down the utility maximization problem and corresponding Lagrangian function. c) Solve for optimal bundle, X* and y* as a function of Px, Py, and M.
1. Suppose the utility function for goods q1 and q2 is given by U(q1, q2) = q1q2 + q2 (a) Calculate the uncompensated (Marshallian) demand functions for q1 and q2 (b) Describe how the uncompensated demand curves for q1 and q2 are shifted by changes in income (Y) or the price of the other good. (c) Calculate the expenditure function for q1 and q2 such that minimum expenditure = E(p1, p2, U) (d) Use the expenditure function calculated in part...
1) Optimization problem 1 Max U(x, y) = x1^0.5 + x2^0.5 s.t. x1 + x2 =16 Find the optimum bundle; check if there is a minimum or a maximum. 2) Give the interpretation of the expenditure function, explain and show its properties. Draw the diagram of the expenditure function. Derive the compensated demand function for x1 and x2 E( p, u) = p(p1. p2)^0,5 and the uncompensated demand function. 3) Derive the expenditure function when the direct utility function...
Part 3: Longer Problems 1. Suppose that the utility function of a typical visitor to an amusement park is Ur, y) = r - (1/2)r+ y, where r is the number of rides and y is expenditure on all other goods. The current price per ride is p. Each visitor has income of M. The MU, = 1-r. (a) Derive the Marshallian or ordinary demand function for rides. Com- ment the demand function. (b) On a diagram, graph the visitor's...
Suppose you have a total income of I to spend on two goods x1 and x2, with unit prices p1 and p2 respectively. Your taste can be represented by the utility function u left parenthesis x subscript 1 comma x subscript 2 right parenthesis equals x subscript 1 cubed x subscript 2 squared (a) What is your optimal choice for x1 and x2 (as functions of p1 and p2 and I) ? Use the Lagrange Method. (b) Given prices p1...
Suppose that the utility function of a typical visitor to an amusement park is U (r, y) = r - (1/2)p2 + y, where r is the number of rides and y is expenditure on all other goods. The current price per ride is p. Each visitor has income of M. The MU, = 1-r. (a) Derive the Marshallian or ordinary demand function for rides. Com- ment the demand function. (b) On a diagram, graph the visitor's optimal number of...
Part 3: Longer Problems 1. Suppose that the utility function of a typical visitor to an amusement park is Ur,y) = r - (1/2)r? + y, where r is the number of rides and y is expenditure on all other goods. The current price per ride is p. Each visitor has income of M. The MU=1-r. (a) Derive the Marshallian or ordinary demand function for rides. Com- ment the demand function. (b) On a diagram, graph the visitor's optimal number...
1. (20 points) Mac has utility over x; and x2 given by u(x1, x2) = min . If P. = $1. P. = $1. and I = $100. find the value of xı* (Hint: This is Leontief utility, the kind with right-angled indifference curves) 2. (10 points) If P, = $4, P2 = $2, and I = $20, and my utility is given by u(x1, x2) = 4x1 + 3x2, find x* (Note: I'm asking for optimal consumption of Good...
2) Chimichanga Fest Your utility function is given by U-X,X, where xi s your consumption of Chimichangas and x, is your consumption of all the other goods in the economy. Yes, you spend 60% of your budget on Chimichangas, which is totally reasonable after the Dumpling House tragedy. a) Solve the utility maximization problem, finding the uncompensated demand for x, & x, and the indirect utility function in terms of p,, p, and Y. b) Solve the expenditure minimization problem,...
2) Assume that utility is given by Utility-U(X,Y)-X03yo7 a) Calculate the ordinary demand functions, indirect utility function, and expenditure function. b) Use the expenditure function calculated in part (a) together with Shephard's lemma to compute the compensated demand function for good X. Use the results from part (b) together with the ordinary demand function for good X to show that the Slutsky equation holds for this case. c) d) Prove that the expenditure function calculated in part (a) is homogeneous...