Question

In: Economics

Let assume that a consumer has a utility function u(x, y) = xy, and px =...

Let assume that a consumer has a utility function u(x, y) = xy, and px = 1 dollar, py = 2 dollars and budget=50. Derive the followings. (3 points each)

1) Marshallian demands of x and y

2) Hicksian demands of x and y

3) Indirect utility function

4) Expenditure function

5) Engel curve

Solutions

Expert Solution


Related Solutions

Jim’s utility function is U(x, y) = xy. Jerry’s utility function is U(x, y) = 1,000xy...
Jim’s utility function is U(x, y) = xy. Jerry’s utility function is U(x, y) = 1,000xy + 2,000. Tammy’s utility function is U(x, y) = xy(1 - xy). Oral’s utility function is -1/(10 + xy. Billy’s utility function is U(x, y) = x/y. Pat’s utility function is U(x, y) = -xy. a. No two of these people have the same preferences. b. They all have the same preferences except for Billy. c. Jim, Jerry, and Pat all have the same...
Suppose that a consumer has utility given by U(X, Y ) = XY + 10Y and...
Suppose that a consumer has utility given by U(X, Y ) = XY + 10Y and income of $100 to spend on goods X and Y.   The prices of X and Y are both $1 per unit. Use a Lagrangian to solve for the optimal basket of goods.   Suppose that the price of X increases to $5 per unit. Use a Lagrangian to solve for the new optimal basket of goods. Find the total effect of the price change on...
Welfare Measures Consider a consumer with utility function of the form u(x,y) = √xy. Where x...
Welfare Measures Consider a consumer with utility function of the form u(x,y) = √xy. Where x is the number of hamburgers and y the number of soft drinks. (a) Find the compensated demands. (b) Calculate the Compensated Variation (CV) when the price of soft drinks increase from $1 to $4. (Assume that the utility at the original price level is equal to 2 and the price of hamburgers is equal to $4) (c) Is the consumer better-off or worse-off after...
Esther consumes goods X and Y, and her utility function is      U(X,Y)=XY+Y For this utility function,...
Esther consumes goods X and Y, and her utility function is      U(X,Y)=XY+Y For this utility function,      MUX=Y      MUY=X+1 a. What is Esther's MRSXY? Y/(X + 1) X/Y (X + 1)/Y X/(Y + 1) b. Suppose her daily income is $20, the price of X is $4 per unit, and the price of Y is $1 per unit. What is her best choice?      Instructions: Enter your answers as whole numbers.      X =      Y =      What is Esther's utility when her...
Consider a consumer with the utility function U(X, Y) = X^2 Y^2 . This consumer has...
Consider a consumer with the utility function U(X, Y) = X^2 Y^2 . This consumer has an income denoted by I which is devoted to goods X and Y. The prices of goods X and Y are denoted PX and PY. a. Find the consumer’s marginal utility of X (MUX) and marginal utility of Y (MUY). b. Find the consumer’s marginal rate of substitution (MRS). c. Derive the consumer's demand equations for both goods as functions of the variables PX,...
Suppose a consumer has a utility function given by u(x, y) = x + y, so...
Suppose a consumer has a utility function given by u(x, y) = x + y, so that the two goods are perfect substitutes. Use the Lagrangian method to fully characterize the solution to max(x,y) u(x, y) s.t. x + py ≤ m, x ≥ 0, y ≥ 0, where m > 0 and p < 1. Evaluate and interpret each of the multipliers in this case. What happens to your solution when p > 1? What about when p =...
assume that U(x, y) = xy, Px = 1, Py = 4 and B = 120....
assume that U(x, y) = xy, Px = 1, Py = 4 and B = 120. Using the Bordered Hessian matrix, verify that the second-order conditions for a maximum are satisfied. Show steps.
Suppose a consumer has a utility function u(x, y) = 2x + 3y. The consumer has...
Suppose a consumer has a utility function u(x, y) = 2x + 3y. The consumer has an income $40 and the price of x is $1 and the price of y is $2. Which bundle will the consumer choose to consume? Determine the demand functions for x and for y. Repeat the exercise if, instead, the consumer’s utility function is u(x, y) = min{x, 2y}.
Jack has a utility function u(x,y) = xy, and an endowment of (2,4). He has no...
Jack has a utility function u(x,y) = xy, and an endowment of (2,4). He has no other income. (a) Calculate the demands when the prices are px = 2, py = 4. (b) What are the net demands for the prices from (a)? (c) Let the prices be variables. Calculate the demands as functions of the prices. (d) Now let the prices and the endowments be variables. Calculate the demands as functions of the endowments and the prices.
Suppose that the utility function of a consumer is U(x,y) = x ¼y ¾, where x...
Suppose that the utility function of a consumer is U(x,y) = x ¼y ¾, where x and y are the quantities of the good X and good Y consumed, respectively. The consumer's income is 400. (a) What is the demanded bundle when the price of good X is 10 and the price of good Y is 10? (b) Redo part (a) when the price of good X is doubled? (c) Redo part (a) when the price of good Y is...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT