8. Show that if strict preferences > over three outcomes x, y and z, do not satisfy transitivity, so that x > y > z > x, then these preferences cannot be represented by a utility function.
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- Dear Expert hero pro Hand written solution is not allowed.Let the following table represents the total utility of a given consumer, in the cardinal utility approach. Q 1 2 3 4 5 6 7 TUX 8 14 18 20 20 18 16 TUY 6 10 13 15 16 16 14 MUX MUY MUX/PX MUY/PY Calculate the MUX and MUY and fill the table in the 4th and 5th rows. If the two products (X&Y) are free goods how many of X and Y should the consumer take to maximize utility? What is the maximum utility of X and Y if they are free? Let now price of X is 4 birr per unit and price of Y is 2 birr per unit. Calculate MUX/PX and MUY/PY and fill the 6th and 7th row. Assuming the consumer has any amount of money (enough budget) how many of X and Y should the consumer buy, to maximize utility? What is the total utility of X and Y? Let now price of X is 4 birr per unit and price of Y is 2 birr per unit and budget of the consumer for consumption of X and Y is 20 birr. Given budget constraint how many of X and Y should the consumer buy to maximize utility?5. Suppose a preference relation is represented by a utility function u(x₁, x₂) = x₁ + x₂. Explain why the function -u(x₁, x₂) = −x₁ - x₂ does not represent the same preference relation. It is enough to explain using two appropriate bundles.
- As a consumer you have RM34 per month to spend for snack i.e. either pizzas which costs RM6 each or chicken burger which cost RM4 each. Suppose further that your preference is given by the following Total Utility Table Quantity 1 2 3 4 5 6 7 Pizza 60 108 138 156 162 166 166 Chicken Burger 44 76 100 120 136 148 152 First, graph the budget constraint with Pizzas on the horizontal axis and Chicken burger on the vertical axis. What are the intercepts at horizontal axis and vertical axis. Using the table, please show the Marginal Utility of Pizzas and Chicken Burger for every quantity demand. Using the utility maximizing rule to identify the consumer equilibrium, that is, combination of pizzas and chicken burger that will maximize your Total Utility. Confirm that the consumer equilibrium generates the highest combined total utility of any affordable combination of goods.Problem 2 Suppose that John's preferences over meat (M) and vegetables (V) are represented by the following utility function U(M,V) = a ln(M) + (1 − a) ln(V) where 0 < a < 1. ¹No claim of realism is made for the numbers in this example. 1 (a) Write down the Lagrangian for John's optimization problem. (Recall that John max- imizes utility given an income, I, and prices på and på for the goods.) (b) Solve for John's optimal consumption bundle (M*, V*) (as a function of income and prices) using the Lagrangian method. = (c) Suppose a = . Suppose also that John has income I = 1 and pv 2. What is the value of John's optimal happens if John's income doubles to I = 400? 200 and faces prices p consumption bundle? What =1. Sam is going to Baltimore for the day to watch his favorite baseball team (Orioles). Sam loves his Orioles, but he is addicted to drinking beer (B) and eating hotdogs (D) while watching his team. His utility function is: U = (B*D)1/2 a. Suppose Sam has $50 to spend on beer and hotdogs. Beer costs $5 a mug and a hotdog costs $4. Draw Sam's budget constraint. b. Suppose Sam spends all of his income on beer. How many mugs of beer can he buy? What is his utility? c. Will Sam's income allow him to reach a U = 5? d. If Sam buys 4 hotdogs, how many mugs of bear can he buy? What is his utility? e. What is the combination of beer and hotdogs that yield the highest utility? 2. Firm A's Price $20 $15 $20 $40 profit $35 profit Firm B's Price $37 profit $39 profit $15 $49 profit $38 profit $30 profit $35 profit a. Firms A and B are member of an oligopoly. Which solution will Firm A and B select? b. Is there a Nash equilibrium? If so, what is it? c. Which solution will Firm A and B select if Firm…
- 4. What kind of preferences are represented by a utility function of the form u(r1, r2) = VI1 + x2? WWhat about the utility function v(r1,r2) = 13.r, + 13.r2? %3D %3D4. Maximize utility U = xy subject to 4x+3y=60, where x and y are the two consumption goods, 4 is the price of good x, 3 is the price of good y, and 60 is the budget. a) Set up the Lagrangian objective function. How much is the utility-maximizing consumption bundle? b) Show that the second-order condition/s is/are met (Use |Ħ₂ to identify whether it is a maximum or a minimum). c) What is the maximum utility?3
- 12) A consumer’s preferences are given by U(X,Y) = X0.6Y0.4. The price of X is 4, and the price of Y is 5. The consumer has an income of $2000.a) What is the utility maximizing choice of X and Y?b) How would the utility maximizing choice change if price of X falls to 3 because of a pricesubsidy?c) Given the answers to the previous parts plot a linear demand function for X.d) Show that the consumer would prefer the cash equivalent of the price subsidy in part b.ayesha derives utility from travelling and outdoor dinning o weekends as given utility function U(t,d)=TD.the price of a day spent travelling is $160{Pt=160} and price of dining outdoor $200{Pd=200}.ayesha annual budget for this is $8000. find ayesha's utility maximizing choice of days travelling and dining outside. and alsoo find uutility level from consuming that bundles .show findings graphicallyi. Write down the Lagrangian form and solve the utility maximization problem. ii. Assume that the income increases from 100 to $101. What is the increase in the optimal value of u(x,y)?