The utility function of a consumer is given as follows. U(x, y) = x²y³, MU, = 2xy3 and MU, =3x?y?.a.Derive the demand functions for good x and good y.b. Draw a demand curve.Draw an Engel curve. Is good x a normal good?С.

It tells the inverse relation between quantity and price of the commodity.

Answered: The utility function of a consumer is…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose a consumer utility function is given by U(X,Y)=XY+8X the price of good X and Y are 2 birr and 6 birr respectively the consumer has total income of 160 birr to be spent on two goods A) find the utility maximizing quantities of good X and Y B) find MRXSY at equilibrium
Consider a market with two goods, x and z. The consumer’s utility function is U = x^0.2z^0.8 A. Derive the demand function for x and z. B. Let ? = 2, = 4 and = 50. Find the equilibrium quantities demanded of x and z.
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Suppose Cenk consumes only two goods, Good X (inferior good) and Good Y (normal good). Given that these goods are imperfect substitutes of each other and he chooses the bundle, which maximizes his satisfaction, answer the following questions. a. For Cenk, draw a hypothetical equilibrium using his budget constraint and indifference curves and show his optimal bundle. (Place Good X on the horizontal and Good Y on the vertical axis.) b. Say, the price of Good X decreases. Show the Income and Substitution effects of this price change on Cenk's optimal
Question 2. A consumer has the utility function U(q1,q2) = q10.5 + q2Assume p2 = 1 and Y = 100. What is the equivalent variation of a price increase for good 1 from 1 to 4?
he Calculus of Utility Maximization and Expenditure Minimization -End of Appendix Problem uppose that there are two goods, X and Y. The price of X is $2 per unit, and the price of Y is $1 per unit. There are two onsumers, A and B. The utility functions for the consumers are UA(X,Y)= X05.05 UB(X,Y)= X0.8y0.2 Consumer A has an income of $100, and Consumer B has an income of $300. Using Lagrangians, solve for the optimal bundles of goods X and Y for both consumers A and B. a. The optimal bundle for consumer A is X = 25 and Y* = 50 - b. The optimal bundle for consumer B is X = 120 and Y* = 60
Part 1 Using this information, Create a line plot of the solutions with the price of good Y on the y-axis and the quantity of good Y on the x-axis on a sheet of paper (connect the dots). Calculate the slope of this curve. Be sure to put a negative sign in your answer if you need to. Part 2 Is this line you found the demand curve?
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Imagine Billy eats brownies (B) and cookies (C) and considers them to be perfect substitutes. Brownies yield him four times more utility than cookies. Which of the following equations could describe his utility function? U= 0.25B + C O U=B+ 0.25C U = B'C OU = BC4 %3D
16.Suppose the market for a good is composed of 1,000 identical consumers. The market's demand curve is given by QM = 150,000 – 25P. What is the equation for an individual consumer's demand curve? A) Q = 150,000,000 – 25,000P B) Q = 6,000,000 – 40P C) Q = 6- 4P D) Q = 150 –0.025 17.There are 100 consumers in the market for good X. each with a demand curve given
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The utility function of a consumer is given as follows. U(x, y) = x?y3. MU, = 2xy3 and MU, 3x?y2. %3D %3D a. Derive the demand functions for good x and good y. b. Draw a demand curve. Draw an Engel curve. Is good x a normal good? C.