Suppose that the utility function for two goods X and Y is given by U = x2y. (a) Write the equation of the indifference curve for a consumer who purchases 8 units of X and 25 units of Y. (b) If the consumer purchases 100 units of Y, how many units of X must be purchased to retain the same level of utility?
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- 2) Suppose there are two consumers in an economy: consumer A and consumer B. They have two goods (x and y) allocated between them. A has 5 units of x, B has 15 units of x. A has 5 units of y, B has 5 units of y. Consumers have identical utility functions given by U=x*y. a) Draw the Edgeworth box showing the current allocation of the two goods. Put consumer A in the lower left-hand corner, and consumer B in the upper right-hand corner. b) To your Edgeworth box add the two consumers' indifference curves going through the initial allocation point, clearly showing that the allocation is not efficient. Explain why it is not efficient, using the MRS calculations. c) Suggest a trade that would increase both consumers' utility. (Several correct answers are possible). Is your proposed allocation efficient? d) What does the contract curve look like in this economy? Derive its formula and add its graph to your Edgeworth box.1. Consider a pure exchange economy with two goods and two consumers. Let F denote food and C denote clothing. Lacy has the utility function U(F, C) = F 1/3 C 2/3 . Roy has the utility function V (F, C) = F 2/3 C 1/3 . Each consumer has an initial endowment consisting of 9 units of F and 9 units of C. Normalize the price of F to one. Let P denote the price of C. (a) Is the initial endowment a Pareto efcient allocation of F and C between the two con sumers? Explain briefy. (b) What is each consumer’s demand for F and C as a function of P? [Hint: the wealth of each consumer is 9 + 9P.] (c) What is the price of C in a competitive equilibrium? (d) What is the allocation of F and C between the two consumers in a competitive equilibrium?Answer the question on the basis of the following marginal utility data for products X and Y. Assume that the prices of X and Y are $4 and $2, respectively, and that the consumer's income is $18. Units of X 1 2 3 4 5 Marginal Utility, X Multiple Choice 20 16 12 8 6 4 4 of X and 5 of Y What quantities of X and Y should be purchased to maximize utility? O 2 of X and 1 of Y O 2 of X and 6 of Y Units of Y 1 2 3 4 5 6 O2 2 of X and 5 of Y Marginal Utility, Y 16 14 12 10 8 6
- A market demand function is given by the equation QD = 180 – 2P. Find the value of consumer surplus if price is equal to 65. Illustrate your demand curve and the area of consumer surplus. Identify the area of consumer surplus, the price at which demand is zero, the level of demand if price was zero and the slope (show calculation if required).Consider a product market with three consumers A, B and C with demand function PA = 6 – QA, PB = 6 – 2QB and PC = 12 – QC respectively, where P is the price in dollars and QA, QB and QC are the quantities demanded by Consumer A, B and C respectively. The marginal cost of the product is constant at $4. (i) If the product is public good, analyse the product and determine the optimal quantity of the product in the market.(ii) How will your answer be different if the product is a private good instead? (Hi there, may I requst for a detailed step by step explanation as i struggle with this topic. Thank you)Consider a product market with three consumers A, B and C with demand function PA = 6 – QA, PB = 6 – 2QB and PC = 12 – QC respectively, where P is the price in dollars and QA, QB and QC are the quantities demanded by Consumer A, B and C respectively. The marginal cost of the product is constant at $4. (i) If the product is public good, analyse the product and determine the optimal quantity of the product in the market.(ii) How will your answer be different if the product is a private good instead?
- A consumer's utility only depends on the consumption of goods A and B according to the following Cobb - Douglas utility function: U(A, B) = A3/5 B 2/5. The price of goods A and B are $10 and $10, respectively. The consumer has a budget of $1500 that he can use to consume the two goods. a) Calculate the optimal bundle and maximized utility for the consumer. b) A new tax of $5 is imposed on the price of good B. Compute the new optimal bundle of good A and B for the same consumer. What is the utility loss due to the tax? c) Show that the consumer would prefer a lump sum income tax that raises the same revenue of $200 as the tax on good B.Translate the following monetary payoffs into utilities for a decision maker whose utility function is described by an exponential function with R = 250: –$200, –$100, $0, $100, $200, $300, $400, $500.Three decision makers have assessed utilities for the following decision problem (payoff in dollars): The indifference probabilities are as follows: Plot the utility function for money for each decision maker. Classify each decision maker as a risk avoider, a risk taker, or risk-neutral. For the payoff of 20, what is the premium that the risk avoider will pay to avoid risk? What is the premium that the risk taker will pay to have the opportunity of the high payoff?
- The graph of a company's profit function is shown. Use the graph to answer the following questions about points A, B, and C. P(x) 5000 P(x) 3000 B. 1000- -1000 - 100 TA 200 300 400 Units (a) Rank from smallest to largest the amounts of profit received at these points. O A, B, C O A, C, B О в, А, С О в, с, А О С, А, В О С, в, А Explain your choices. O The profit is represented by the slope at each point. O The profit is represented by the P(x) coordinates. O The profit is represented by the x coordinates. Note whether any point results in a loss. (Select all that apply.) none of these DollarsThe supply and demand equations of a good are given by the following formulas P=2Qs +48 P= -6QD+ 160 Find the equilibrium price and quantity. The equilibrium quantity is. (Type an integer or a decimal.) ***Consider an individual facing the prospect of having high income, YH > 0, with probability 7 and low income, YL, with probability 1 – T, YH > YL. Prior to learning whether realized income is high or low, the individual is able to go into the market and purchase (or sell) two types of assets. Let the Asset 1 have a return structure such that it pays R1.H units of goods if y = YH and pays R1,L units of goods if y = YL. Similarly, let Asset 2 have a return structure such that it pays R2.H units of goods if y = YH and pays R2,L units of goods if y to spend in the asset market but this wealth is not storable and hence cannot be save to purchase consumption goods. Denote by a1 the amount of Asset 1 purchased by the individual and az the amount of Asset 2 purchased by the individual. The individual's problem is to maximize the expected utility from consumption sub- ject to the constraints that consumption must be financed out of income and the realized return from the asset portfolio as well…