Question

1. Basket A contains 1 beer and 5 pizzas. Basket B contains 5 beers and 1 pizza. Basket C contains 3 beers and 3 pizzas. Assume throughout that tastes are monotonic.

On Monday, Bob is offered a choice between basket A and C, and he chooses A. On Tuesday he is offered a choice between basket B and C, and he chooses B.

1. (c) Suppose that Bob’s preferences satisfy a weak convexity assumption (averages are at least as good as extremes). Suppose also that his preferences have not changed from Monday to Tuesday. Can we conclude anything about the precise shape of one of Bob’s indifference curves?

   Consider the utility function U (x, y) = x + y, where x are units of beer and

   y are units of pizza.

2. (d) What is the equation of an indifference curve?

3. (e) What is the MRS at basket A? What is it at basket B? What is it at basket C? What is the geometric equivalent of the MRS? What is the interpretation of the MRS?

4. (f) Can this utility function capture preferences that this give rise to con- clusion about the shape of one of the indifference curves in part c)?

5. (g) What is the equation of an indifference curve?

6. (h) What is the MRS of this function? Note, MUx = 2x and MUy = 2y.

7. (i) Do these tastes have diminishing marginal rates of substitution? Are they convex?

8. (j) Can this utility function capture preferences that this give rise to con- clusion about the shape of one of the indifference curves in part c)?

9. Do these two utility functions represent different preference orderings?

   Now consider tastes that are instead defined by the function U (x, y) = x2 + y2, where x are units of beer and y are units of pizza.

Answer 1

(C).

In the event that the given suspicions are valid, at that point the lack of concern bend of weave's inclination would straight line( descending slanting).

Consider the utility capacity U(x, y) = x* y The lack of concern bend is given by the mixes of x and y keeping utility steady. So let us consider U(x,y)= where U is a steady estimation of utility. (0). In this way, the condition of the lack of concern bend is :

Cl=x+y

Separating, dU = dx + dy 0 = dx +dy ( as utility is consistent) dx = - dy 7/7=-1

(e) MRS is the total estimation of 2 I,e, 1

Accordingly, MRS stays steady all through for this situation as it doesn't rely upon estimation of x or y. Consequently, MRS at basket An is equal to MRS at basket B which is proportionate to MRS of basket C. It doesn't rely upon what number of lager or pizzas are there in which pack. It is steady all through. The geometric proportionate to the MRS is given by the outright slant of the impassion bend as demonstrated as follows.

The Marginal Rate of Substitution (MRS) is the rate at which a customer is prepared to trade various units of good X(beer) for one a greater amount of good Y(pizzas) at a similar degree of utility.

f) Weak convexity presumption implies the midpoints are at any rate on a par with limits. In the event that An and B lie on same lack of concern bend, it will mean C (the normal) is as at any rate in the same class as An or B. It is levelheaded to pick An over C and the following day, B over C without influencing the preferences. It implies the lack of concern bend is a straight line. Therefore, this utility capacity catch inclinations that offer ascent to the decision about state of aloofness bends partially C. This impassion bend is likewise a straight line.

Presently, another utility capacity

(g) The condition of a lack of interest bend portrays various blends of the two merchandise at a given degree of utility. let U(x,y)=k which is steady.

x^2+y^2=k

                 differentiating

0=2x dx+2ydy (AS UTILITY CONSTANT)

                                   x dx=-y dy

                                   

(h) MRS=

(i)      

                  hence no dimensing MRS and convexity does not hold.

(j) NO in light of the fact that partially c it is curved yet to some degree (I) it is cancave

x I adors N

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