Suppose firm T’s utility function is: U(X,Y) = X0.4Y0.6. The firm has a budget of $100,...

Suppose firm T’s utility function is: U(X,Y) = X0.4Y0.6. The firm has a budget of $100, and the price of material Y is $20 and the price of X is $10. a) What is the optimal combination of inputs of X and Y for this firm? b) Suppose the price of Y and X are now $10 and $20, respectively. What effect will this have on the firm’s optimal input combination? c) Illustrate the answers to the preceding questions with the use of isoquant/isocost diagram.

Expert Solution

Rahul Sunny answered 1 year ago

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 =...

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...

Suppose an individual has the following utility function: U(X,Y) = 2XY. Draw the budget constraint when...

Suppose an individual has the following utility function: U(X,Y) = 2XY. Draw the budget constraint when the price of each unit of X and Y are 5 and 4, and income is 120. Find the choice that maximizes utility.

Suppose a consumer's utility function is given by U ( X , Y ) = X...

Suppose a consumer's utility function is given by U ( X , Y ) = X 1 2 Y 1 2. The price of X is PX=8 and the price of Y is PY=5. The consumer has M=80 to spend. You may find that it helps to draw a graph to organize the information in this question. You may draw in the blank area on the front page of the assignment, but this graph will not be graded. a) (2...

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 a consumer has preferences represented by the utility function U(X,Y) = X(^2)Y Suppose Py =...

"Suppose a consumer has preferences represented by the utility function U(X,Y) = X(^2)Y Suppose Py = 1, and the consumer has $360 to spend. Draw the Price-Consumption Curve for this consumer for income values Px =1, Px = 2, and Px = 5. Your graph should accurately draw the budget constraints for each income level and specifically label the bundles that the consumer chooses for each income level. Also for each bundle that the consumer chooses, draw the indifference curve...

Suppose a consumer’s utility function is given by U(X,Y) = X*Y. Also, the consumer has $200...

Suppose a consumer’s utility function is given by U(X,Y) = X*Y. Also, the consumer has $200 to spend, and the price of X, PX = 5, and the price of Y, PY = 2. a) How much X and Y should the consumer purchase in order to maximize her utility? b) How much total utility does the consumer receive? c) Now suppose PX decreases to 1.25. What is the new bundle of X and Y that the consumer will demand?...

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}.

Suppose Anne’s utility function for food (X) and clothing (Y) is given by U (X,Y) =...

Suppose Anne’s utility function for food (X) and clothing (Y) is given by U (X,Y) = 4X1/2 + Y and Anne had budget constraint I = PxX + PyY. a. Find Anne’s optimal bundle if Px = 4 and Py = 4 and Anne has I = 60. b. Discuss how the demand for X depends on her income. c. Suppose now that the price of X increases to 8. Find the SE and IE of the price change.

Suppose that an individual has a utility function of the form U = Y½ where U...

Suppose that an individual has a utility function of the form U = Y½ where U is utility and Y is income. a) Calculate the utility level for Y values of $10,000, $40,000, $90,000, $160,000, and $250,000 and then plot the individual’s total utility function. b) This individual is currently earning $90,000 but has a 50-50 chance of earning either $40,000 or $160,000 in a new job. i) Calculate the expected income and utility from the new...

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