For each of the following utility functions, draw an indifference map with 3 indifference curves. Be sure to label your axes, and label your curves as IC1, IC2, and IC3, where U1 < U2 < U3. (5 points each) a. ?(?, ?) = 3? + 5? b. ?(?, ?) = ? 2 + ? 2 c. ?(?, ?) = −? 2 + ln(?) d. ?(?, ?) = min(3?, 5?)
a)
The utility function is given as
This is an equation of a straight line. The goods are a perfect substitute, and hence the ICs are a straight line. The higher the utility, the further away the ICs are from the origin. The three ICs with their respective utilities are:
The indifference map represents the above utility functions for different utilities described above:
===================================================================================
b)
The utility function is given as
This is an equation of a circle. In the positive quadrant, it is concave to the origin. The goods are bad to the consumer, and hence the ICs are concave to the origin. The higher the utility, the further away the ICs are from the origin. The three ICs with their respective utilities are:
The indifference map represents the above utility functions for different utilities described above:
==============================================================================
c)
The utility function is given as
This is an equation of a parabola. In the positive quadrant, it is positively sloped and concave. This implies one of the goods is bad to the consumer, and hence the ICs are concave to the origin. The higher the utility, the further away the ICs are from the origin. The three ICs with their respective utilities are:
The indifference map represents the above utility functions for different utilities described above:
====================================================================================
d)
The utility function is given as
This is an equation of a right-angled curve. This implies one of the goods are perfect complement and used in a fixed proportion, and hence the ICs have a kink. The higher the utility, the further away the ICs are from the origin. The three ICs with their respective utilities are:
The indifference map represents the above utility functions for different utilities described above:
For each of the following utility functions, draw an indifference map with 3 indifference curves. Be...
For each of the following utility functions, draw an indifference map with 3 in curves. Be sure to label your axes, and label your curves as IC1, IC2, and ICs, where difference 1 U2 U (X,Y)=3X+5Y U3. (5 points each) a. U(X, Y) U(X, Y) -X2 + ln(Y) min(3X,5Y) c. d.
carefully 1. Carefully sketch the indifference curves corresponding to the utility functions and the utility levels given below (a) u1 2 and ug 8. (b) ulxi,x) x u8 and ug 512. (c) 2 ules,)InIns u1 0.6931 and ug 2.0794. 4 1. Carefully sketch the indifference curves corresponding to the utility functions and the utility levels given below. (a) u(x1,x2) xx u1 2 and u2 = 8. (b) u(x1,x2) x1x; u1 8 and u2 =512. (c) 2 u(x1,x2)=Inx1 +Inx2; u1 0.6931...
The following graph shows a variety of possible indifference curves (labeled IC1, IC2, and IC3, respectively) for Latasha. Each indifference curve represents a different level of happiness. RASPBERRIES (Pints per month 10 Budget Constraint Best Bundle IC3 C1 0 2 3 456 7 8 9 10 STRAWBERRIES (Pints per month) HelpClear ALl The shape of the indifference curves indicates that the goods strawberries and raspberries must be Suppose the price of strawberries is $3 per pint, the price of raspberries...
4. [25 POINTS]Use separate graphs to draw indifference curves for each of the following utility functions: (a) 6 POINTS] U (x, y) = min{2x + y, 2y + x}. (b) [6 PoINts] U (x,y) = max{2.x + y, 2y + x}. (c) 6 POINTS] U (x,y) = x + min {x, y}. (d) 7 POINTS] In which of these cases are preferences convex? 4. [25 POINTS]Use separate graphs to draw indifference curves for each of the following utility functions: (a)...
For each of the following functions, i) pick three utility levels and draw the precise indifference curves that are associated with the levels of your choice, ii) label the utility level of the lines--you cannot just draw random lines and assign arbitrary utility levels, and iii) give the name of preferences they represent (hint: see figures in textbook chapter 3) 2. u(x,2) -min(xi,x2) 5. u(xi, x2) -xjx2
please answer all questions 2. Draw the graph of an indifference curve map for the utility function U(X,Y)= XY. Put good X on X-axis and good Y on Y-axis. Draw at least 3 indifference curves and label the utility level for each indifference curve. Explain why or why not do the indifference curves cross each other on the map.
For each of the following functions, i) pick three utility levels and draw the precise indifference curves that are associated with the levels of your choice, ii) label the utility level of the lines -- you cannot just draw random lines and assign arbitrary utility levels, and iii) give the name of preferences they represent (hint: see figures in textbook chapter 3). 1. u(x1, 12) = I1 + 2.12 2. u(21, 22) = min(21, 22) 3. u(x1,22) = 21 4....
Draw indifference curves to represent the following consumer preferences. For each set of preferences draw two indifference curves U1 and U2 such like, U1 > U2 e) I like peanut butter and jelly, and have a diminishing marginal rate of substitution. f) I like to consume exactly 5 ounces of peanut butter and 5 ounces of jelly. The further away I get from this point, in any direction, the less happy I am.
1. Consider the following utility functions (a) For each of these utility functions: i. Find the marginal utility of each good. Are the preferences mono- tone? ii. Find the marginal rate of substitution (MRS) iii. Define an indifference curve. Show that each indifference curve (for some positive level of utility) is decreasing and convex. (b) For the utility function u2(x1, x2), can you find another utility function that represents the same preferences? Find the relevant monotone trans formation f(u) (c)...
For each of these utility functions, b. Compute the MRS. c. Do these tastes have diminishing marginal rates of substitution? Are they convex? d. Construct an indifference curve for each of these functions for utility numbers U1 = 10 , U2 = 100 , U3 = 200 . e. Do these utility functions represent different preference orderings? 1. Consider the following utility functions: (i) U(x,y)- 6xy, (ii) U(x,y)=(1/5)xy, MU,--y and MU,--x ii) U(x,y)-(2xy)M 8xy2 and MUy -8x2y MU,-6y and...