solve d,e,f please Thank you (a) Suppose we have preferences U(X, Y) = min [X, 3Y]. Graph/sketch the indifference curvethrough the bundle (X = 30, Y = 30). What is the utility of (30, 30) and explain why theindifference curves look the way they do.(b) What does the Marginal Rate of Substitution tell us about preferences? <(c) Why is the Marginal Rate of Substitution not applicable in this example? <(d) What do we mean by a composite good? What does this composite good look like with thesepreferences? Show and explain.<(e) State the consumer's maximization problem and express this in words.<(f) Now let Px = 10, Px= 20 and income M = 2000. Find optimal X*, Y*, and the resulting Utility(U*). Show your work. <(g) Now let Py = 15. How does optimal consumption (X*.Y*) and utility (U*) change relative to(e)? Explain in simple terms and show in a diagram.<

Here we are given the utility function and the budget of the consumer. As consumer's objective is to…

(d) What do we mean by a composite good? What does this composite good look like with these preferences? Show and explain. (e) State the consumer's maximization problem and express this in words.< (f) Now let Px = 10, Px=20 and income M = 2000. Find optimal X*, Y*, and the resulting Utility (U*). Show your work. <

(d) What do we mean by a composite good? What does this composite good look like with these preferences? Show and explain. (e) State the consumer's maximization problem and express this in words.< (f) Now let Px = 10, Px=20 and income M = 2000. Find optimal X, Y, and the resulting Utility (U*). Show your work. <

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Consumer Choice Theory

Section6.A: Indifference Curve Analysis

Problem 3SQP

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Take Jeremys total utility information in Exercise 6.1, and use the marginal utility approach to confirm the choice of phone minutes and round trips that maximize Jeremys utility.
(a) Suppose we have preferences U(X, Y) = min [X, 3Y]. Graph/sketch the indifference curve through the bundle (X = 30, Y = 30). What is the utility of (30, 30) and explain why the indifference curves look the way they do. (b) What does the Marginal Rate of Substitution tell us about preferences? < (c) Why is the Marginal Rate of Substitution not applicable in this example? < (d) What do we mean by a composite good? What does this composite good look like with these preferences? Show and explain.< (e) State the consumer's maximization problem and express this in words.< (f) Now let Px = 10, Px= 20 and income M = 2000. Find optimal X*, Y*, and the resulting Utility (U*). Show your work. < (g) Now let Py = 15. How does optimal consumption (X*.Y*) and utility (U*) change relative to (e)? Explain in simple terms and show in a diagram.<
solve e, f, and g please Thank you
solve d,e,f please Thank you
4. If we have the utility function, U(x)=(x−7)^2, and we know that there is an indifference set around x = 4 and an upper contour set of x = 6. How to graphically represent this function? I'm confused about how to draw the upper contour set on the graph? I know the concept that upper contour is the area over the convex line, but don't know how to put it on the graph. Could you draw a simple graph to help me identify the upper contour?
(a) Suppose we have preferences U(X, Y) = 10X²/³ Y¹/3, Create a table and graph/sketch the indifference curve through the bundle X = 30 and Y = 30.< (b) The Marginal Rate of Substitution is MRSxy=-2Y/X. For the bundle (X= 30, Y = 30), calculate and then interpret what the value of the MRS means.< (c) Cobb-Douglas preferences are strictly convex. What does this imply about the MRS as we move along the indifference curve? Explain/discuss (you may want to draw a picture). < (d) What are the two conditions (equations) that identify the optimum given these preferences and the consumer's budget constraint? Sketch this in a figure and explain.< (e)_From (d) we can show that optimal demands are: X=½ M/PX and Y = ½ M/Px. (you do not have to derive these, just use the equations I have given you.) Calculate optimal demands (X*, Y*) and utility if Px = 10, Px= 5 and income M = 1200. < (f)_Suppose Px falls to Px = 8 but Py and M are unchanged (Px = 5 and M = 1200). Calculate the new optimal demands…
2. Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3XY². The current market price for X is £10, while the market price for Y is £5. Sally's current in come is £500. (a) Sketch a set of two indifference curves for Sally in her consumption of X and Y. (b) Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope. (c) Determine the X,Y combination which maximises Sally's utility, given her budget constraint. (d) Calculate the impact on Sally's optimum market basket of an increase in the price of X to $15. What will happen to her utility as a result of the price increase?
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1. Marginal Utilities and the MRS: Find the marginal utility of x1, the marginal utility of x2, and the marginal rate of substitution for the following utility functions: 1. U(x,y) = 2x + 3y 2. U(x,y) = ax + by 3. U(x, y) = 2Vx + y 4. U(x,y) = xy 5. U(x,y) = xy 6. U(x,y) = (x + 2)(y+ 1) %3D
4. Consider the utility function U(r,g) r + Iny. (a) Find the marginal rate of substitution. MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of r and y. How do you interpret these functions? How might a consumer choose between e and y as she tries to increase utility by, for example, consuming more when their income increases?
2. Maria likes to have one cup of coffee (x) and two slices of bread (y) each morning. Which of the following utility functions represents Maria's preference for (x, y)? (a) U(x, y) = min(8x, 2y) (b) U(x, y) = min (4x, 2y) - RIGHT ANSWER (c) U(x, y) = min(x, 2y) (d) U(x, y) = min(x, 2y)
21. A consumer has a utility function defined over two goods X and Y. Let the quantity of Good X be x ≥ 0 and the quantity of Good Y be y ≥ 0. The utility function is given below: u(x, y) = xy + 2y. Assume that the consumer has income m and that prices are på and py. (a) Explain whether the preferences underlying this utility function satisfy completeness and transitivity. (b) Explain whether the preferences underlying this utility function satisfy monotonicity and convexity. (c) Find the consumer's Marshallian demands for Good X and Good Y at prices px > 0 and Py > 0. (d) Show that goods X and Y are normal goods and explain whether either good is a substitute for the other. (e) Assume that px 10, Py = 5 and m = 100. Suppose that px increases to px = 15, how much of the change in demand for Good X is via the substitution effect and how much is via the income effect? Note: You may assume an interior solution (i.e. x > 0 and y> 0). =