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- 1.a Assume that a person’s utility function is given by the following function: ??=3?^(2/3)?^(1/3) Assume also that the price of X is £3, and the price of Y is £3 and that the budget is £45. What is the optimal amount of goods X and Y that should be purchased with this budget? b) Assume now that the price of good X is PD, while all other conditions remain the same. Find the optimal amount of good X that should be purchased for a generic price PD. In other words, find the individual demand function for good X. 1.b Assume now that the price of good X is PD, while all other conditions remain the same. Find the optimal amount of good X that should be purchased for a generic price PD. In other words, find the individual demand function for good X.4. Aaron and Burris have the following utility functions over two goods, x and y. Aaron’s utility function: UA(xA, yA) = min{xA/3, yA} Burris’s utility function: UB(xB, yB) = 9xB + 3yB Aaron’s endowment is eA = (2, 4). Burris’ endowment is eB = (10, 8). In an Edgeworth Box diagram, show which allocations are in the core. Solve for the set of Pareto optimal allocations (i.e. the contract curve) in the Edgeworth Box. Illustrate the contract curve in an Edgeworth Box diagram. Let good y be the numeraire (i.e. set py = 1 and let px = p). Solve for the Walrasian competitive equilibrium allocation and price ratio.5. Sheila and Bruce are taking a canoe trip. Sheila brought 10 boxes of peanuts (x) and 15 bags of chips (y). Sheila's utility function is U*(x,y) = lnvx*+ Invy°. Bruce also brought 20 boxes of peanuts and 5 bags of chips. Bruce's utility function is UB(x.y) = min[x', y'I. a) Illustrate the endowment point and draw a sample set of indifference curves through the endowment point. b) If Sheila and Bruce trade what will be the pattern of mutually beneficial trade? c) If the terms of trade are the number of bags of chips (y) per box of peanuts (x) then what is the largest value that these terms can be for a mutually beneficial trade in this economy? d) Find one mutually beneficial trade where the terms of trade are 1 bag of chips (y) per 2 boxes of peanuts (x). Suppose that Sheila and Bruce set up two competitive markets for peanuts and chips. Below you will show that if the price of peanuts (x) is $1 and the price of chips (y) is $2 then the markets for both peanuts and chips will clear.…
- 1 Alice has a monthly lunch budget of 360 dollars which she spends on either burgers (B) or pizza (Z). The price of each pizza is 16. dollars and the price of each burger is 8 dollars. Alice's utility is given by: u(B, Z) = B'/2 +4Z!/2 + 47!/2 a) Find Alice's budget constraint. Set up the Lagrangian and find her optimal consumption. What is her new consumption if the price of burgers becomes 16 dollars?Question 2 True or False Provide a brief explanation For the Cobb-Douglas utility function the optimal choice of good i is independent of the price of good j. Full explain this question very fastQuestion 1 Consider an economy with two goods t = 1,2. Whenever an individual consumes ₁ units of good 1 and ₂ units of good 2, their utility is given by u(x₁, x2) = aln x₁ + ln x2, where a > 0 is a free parameter. (i) How does the parameter a affect the marginal rate of substitution between goods 1 and 2? Explain intuitively how does the relative preference for goods 1 and 2 change as the parameter a increases.
- 1. George is a musician who enjoys playing two different instruments. His utility function is given by U(G,S) = 8G¹/² + S, where G and S denote guitars and sitars, respectively. The prices of guitars and sitars are PG & Ps respectively. For the following consider guitars to be the good on the horizontal axis. a. Set up George's cost minimization problem when he wants to achieve a utility level (Ū = 28), which he considers to be consistent with a "reasonable" lifestyle. Be sure to identify what he is minimizing and what is serving as his constraint. b. Given your answer to part (a), find the bundle of goods George would consume to achieve a utility level 28, while minimizing the money he spends (solve this symbolically and then substitute in the numerical values). Also find a symbolic expenditure function, that is, E(PG, Ps, ū) for George. What is the minimum amount he needs to spend given the prices PG = $200 and Ps= $100? c. Now suppose Apple Records gives George a guaranteed income…14. Steve Rogers consumes shiny metal shields, denoted as good s, and blue face masks, denoted as good f. The price of shields is p. = 2 and the price of blue face masks is pf = 2. Steve has an income of m = 100 and preferences over shields and face masks given by the Cobb-Douglas utility function u(s, ƒ) = s₹ ƒ½. (a) Write down Steve's budget line and solve for his optimal bundle of shields and face masks (s*, f*). Show your solution graphically by placing shields on the horizontal axis and face masks on the vertical axis. Label Steve's optimal bundle as bundle "A" and be sure to label all intercepts of the budget line. (b) A fancy new store called Avengers Market opens up down the street and offers to sell shields to Steve for a lower price of ps = 0.5. Solve for Steve's new optimal bundle at these prices. Label it as bundle "C" and label all intercepts associated with the new budget line. (d) The owner of Avengers Market, Bruce Banner, is an intelligent person. Now that Steve has…2. Consider the following utility function: U(Qc,Qr) = Qc - QF Derive the relative demand for two goods as a function of endowments (Ec, Er) and relative prices pe/pPF-
