Which of the following utility functions represent preferences that alwaysresult in an interior solution to the consumer's problem?(a) U(r, y) = 2x +In y(b) U(z, y) = 1+ y(c) U(z, y) = In r+ 2y(d) U(z, y) = riytTrue or False? If good r follows the law of demand, the PCC (as theprice of good r changes) must be upward sloping.(а) True(b) False

Interior solution occurs when the optimal combination of goods and services have positive quantities…

Answered: Which of the following utility…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Which of the following utility functions represents preferences over consumption bundles (X, Y) that violate the assumption of diminishing MRS? (a) U(X,Y) = 3 ln(X) + 5 ln(Y) (b) U(X,Y) = X² + y² (c) U(X, Y) = XY (d) U(X,Y) = X² + Y² (e) U(X, Y) = X¹Y³
Let a consumer's utility function be U (x, y) = x'/²y/2. The consumer's income is I = 160 and prices for the two goods are, respectively, p, = 1 and py = 4. (a) Write down the utility maximization problem and compute the optimal consumption basket. (b) Suppose now the price of good y is equal to p, = 16 (while the price of good r stays constant). Compute the new optimal consumption basket.
3*. Ms Smith likes to drink wine; in particular, a french bordeaux (f) at $40 per bottle and a California varietal wine (c) priced at $8. She allocates $600 to these two each month; and her utility is: U(ƒ, c) = ƒ²/³ c¹/³ (a) Write out her (constrained) utility maximization problem. Solve for the optimal consumption of wine f and c.
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Suppose that a consumer has the utility function U(X,Y)= 2X 1/2 y 1/2 for X>0 and Y> 0. Which of the following utility functions would not represent the same preferences? U(X,Y)= 2(X + Y) 1/2 U(X,Y)=2x1/2y 1/2 - 100 O U(X,Y)= In 2 + InX+ In Y O U(X,Y)= X 1/2 y 1/2 O U(X, Y) = 4XY
Consider a person who consumes two goods, x and y, and has a utility function given by U(x, y) = In(x)+y. This person has an income of $100 and faces a price of $0.50 for good x and $1 for good y. Price of x then rises to $0.60. Solve for the compensating variation (CV) and equivalent variation (EV) of this price change. Show your work.
Bob has utility function U(x,y)=x2+y over goods x and y a) Do we have a name for this type of utility function? Are Bob's preferences well-behaved? b) Let Bob have budget I=$60, and let prices be Px=$30, Py=$10. Find Bob's optimal basket of goods x and y. Is this an interior or corner solution? c) What will happen if the price of good y doubles? [Think about: can we use this utility function to describe preferences over pet snakes and pet mice?]
A consumer has utility (see image) on ice creams (x) and cakes (y). (a) Are the indifference curves bowed towards the origin? (b) Derive his demand function (as a function of prices px, py and budget I) for ice cream (x). (c)(Looking at the demand function you found in (b), Is ice cream a normal good? Are ice cream and cakes substitutes or complements? Calculate the income elasticity of market demand at the point px = 2, py = 1 and I = 12.

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