1) Use the graph below to explain why, if all assumptions about preferences are met, thick indifference curves are not possible. Hint: take two points (bundles) on the graph. >XI
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- Q12 please help quick Consider a utility function for apples and bananas. You are given the following three bundles: (12, 4), (4, 12), and (8, 8). Under the standard assumptions of the well-behaved preference relationship. you should strictly prefer (8, 8) to (12, 4) and (4, 12). Briefly explain why?J 4 True or false? Be sure to explain your answer in detail. Suppose the utility function u(x1, x2) = 2x1x2 represents a consumer's preferences. Then the utility function v(x1,x2) = x1x2 also represents the same consumer's preferencesRM2 1. Assume Good X and Good Y are perfect complements and both are normal goods. Suppose the price of X increases while the price of Y remains unchanged. On a preference map, a. demonstrate the change in the optimal consumption bundle. b. On a separate graph, decompose the substitution effect and the income effect.
- Reese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) is represented by the utility function: u(x, y) = xy + x + y Which of the following is NOT true about Reese’s preference? (a) The MRS decreases when x increases.(b) The preferences are homothetic.(c) The marginal utility of y is higher when x = 10 than when x = 5.(d) For any a > 0, Reese prefers the bundle (x =a/2 , y = a/2 ) over either the bundle (x = a, y = 0) or (x = 0, y = a).First household m=$2,500 per month, spends $125 dollars per month on electricity. Second household m=$10,000 per month and spends $200 per month on electricity. p1=0.1 and p2=1 x1=consumption of electricity and x2=everything else The preferences over electricity and other goods is described by a Cobb- Douglas utility function. What are the parameters of the utility function for each of the two households?7.A college football coach says that given any two linemen A and B, he always prefers the one who is bigger and faster. Is this preference relation transitive? Is it complete? 8.Explain why convex preferences means that “averages are preferred to extremes. 9.If good 1 is a “neutral,” what is its marginal rate of substitution for good 2?
- Assume that Rossi consumes only bananas and avocado. Fortunately, she likes both goods. The consumption bundle where Rossi consumes x1 units of bananas per week and x2 units of avocado per week is written as (x1, x2). In fact, Rossi’s preferences can be represented by the utility function u (x1,x2 )=4√(x1 )+ x2 . The price for bananas is $1 per unit and the price for avocado is $2 per unit. Rossi has $24 to spend on the two goods. Write down Rossi’s budget constraint and solve for her optimal consumption bundle.Q.4. Example 1.D.1: Suppose that X = {x,y,z}, B = {{x,y}, {y,z},{x,z}}, C({x,y}_ = {x}, C({y,z}) = {y} and C({x,z})={z} This choice structure satisfies the weak axiom. Nevertheless, we cannot have rationalizing preferences. How do we know if this choice structure satisfies the weak axiom? Given the C({x,y}) = x, C({y,z}), shouldn't C({x,z}) = x? if we have to always make the same choice based on WARP.Natalie is always willing to give up 10 ounces of licorice for 1 ounce of chocolate. Mitchell, on the other hand, will always give up 10 ounces of chocolate for 1 ounce of licorice. Based on this information, answer the following questions: a. Do Natalie's preferences exhibit a diminishing marginal rate of substitution between chocolate and licorice? Why or why not? b. Assuming that Natalie and Mitchell have the same amount of money to spend on chocolate and licorice, who will purchase the most licorice? Why?Natalie is always willing to give up 10 ounces of licorice for 1 ounce of chocolate. Mitchell, on the other hand, will always give up 10 ounces of chocolate for 1 ounce of licorice. Based on this information, answer the following questions: a. Do Natalie's preferences exhibit a diminishing marginal rate of substitution between chocolate and licorice? Why or why not? b. Assuming that Natalie and Mitchell have the same amount of money to spend on chocolate and licorice, who will…
- For the case of two goods, give an example of a utility function U(x1, x2) that represents the preferences of a consumer who regards the two goods as perfect complements. Next, take the transformation f(U) = U³ of the your example utility function and explain if this newly gener ated function represents the original preferences. Further, provide clear arguments supporting or rejecting the claim that "f(U(x1, x2)) must be strongly increasing in (x1, x2)."Assume that Rossi consumes only bananas and avocado. Fortunately, she likes both goods. The consumption bundle where Rossi consumes x1 units of bananas per week and x2 units of avocado per week is written as (x1, x2). A. In fact, Rossi’s preferences can be represented by the utility function u (x1,x2 )=4√(x1)+ x2 . The price for bananas is $1 per unit and the price for avocado is $2 per unit. Rossi has $24 to spend on the two goods. Write down Rossi’s budget constraint and solve for her optimal consumption bundle. B. Now Rossi has $10 more to spend on the two goods ($34 in total), and what is her optimal consumption bundle now? Compare your solution with the previous one. Can you say anything interesting?Could Figure 3.2 be a single indifference curve if preferences are monotonic?
