Which of these utility functions represent the same preferences as (x, y) = x0.5 y0.5 ? a. U(x, y) = -√√xy b. U(x, y) = x+y c. U(x, y) = lnx + Iny d. All of the above represent the same preferences
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- Check if the following utility functions represent the same preferences: u = x+y, v = x3 + y3, w = -1/(x+y). Give reasons for your answer.Lionel eats ham (x) and cheese (y). The utility function U(x,y)=0.25x + 2y^0.5 represents his preferences.a) What is Lionel’s MRS? Holding y constant, how does his MRS change as ham (x) is increased?b) What does your answer in (a) imply about his indifference curves as you hold y constant and increase x? In (c) and (d) you are asked about the Marshallian and Hicksian Demands for cheese (y). Do NOT calculate the demand functions to answer these questions. Use your answers to (a) and (b) to explain your answer. c) Holding prices constant, what is the effect of an increase in income on his Marshallian demand for cheese (y)? Briefly explain your answer.d) Holding prices constant, what is the effect of an increase in utility on his Hicksian demand for cheese (y)? Briefly explain your answer.I am unsure the direction the utility functions would go in , with this specific scenario
- Joe Bob from Workout Problem 4.12 has a cousin Don who consumes goods 1 and 2. Don thinks that 3 units of good 1 is always a perfect substitute for 2 units of good 2. Which of the following utility functions is the only one that would not represent Don's preferences? U(x1, x2) = min{2x1, 3x2}. Ux1, x2) = 20x1 + 30x2 - 10,000. Ux1, x2) = 2x1 + 3x2 + 1000. Ux1, x2) = 4x²2₁ + 12x₁x2 + 9x²₂. More than one of the above does not represent Don's preferences.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) = 4XY1. Is it impossible for two indifference curves to intersect one another? why? 2. What does it mean that preferences are complete? Now would the real-life implica- tions of this assumption look like?
- Explain and differentiate preference and utility.uestion1:Donna and Jim are two consumers purchasing strawberries and chocolates. Jim’s utility function is U (x, y) = xy and Donna’s utility function is U (x, y) = x2y where x denotes strawberries and y denoteschocolates. Jim’s marginal utility functions are MUX=y and MUy=x while Donna’s are MUX=2xy and MUy=x2. Jim’s income is $100, and Donna’s income is $150. What is the optimal bundle for Donna if the price of strawberries is $2 and the price of chocolate is $4? What is the optimal bundle for Jim, and for Donna, when the price of strawberries rises to $3?Question2:Consider a one-period ecoConsider the following utility functions. G(x,y) = x² (1+y) H(x,y) =In(x) + In(2y) +20 L(x,y) = (x+1)1/2 + (y+1) 1/2 U(x,y) = ex+y W(x,y) = 30 x - 4x² + 4 y Z(x,y) = x¹/2 y Which function or functions are homothetic?
- Joyce consumes x1 and x2 together in fixed proportions. She always consumes 1 unit of x2 for 2 units of x1. What is the utility function that describes her preference?Consider the following utility function for goods x1 and x2: u(x1,x2)=(x1+x2)2 What type of preferences does this utility function represent and why?A consumer with income I=120 facing prices pX = 4 and pY = 8 for two goods X and Y (for each good she prefers more to less) chooses optimally to consume 12 units of X. If the prices change and now pX = 6 and pY = 4, what is the possible range for her optimal X consumption? (like, x >/ 7 or 10 >/ x >/7…etc. Use indifference curve analysis on a graph to reason about the possible locations of the new optimal bundle.)
