2. Assume you spend your entire income on two goods X & Y with prices given as Px & Py, respectively. Prices and income (1) are exogenous and positive. Given that U= X'Y', derive the Hicksian demand function for good Y.
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- 1. Assume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U = X2 + Y2 , derive the Marshallian demand function for good Y and evaluate the type of good. 2. Assume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U= X2Y2 , derive the Hicksian demand function for good Y.3. Suppose that initially PX = 2, PY = 8, I = 96 and the Marshallian demand function for good Y is given by Y∗ = (0.5I/ PY)+(0.5PX/PY)− 0.5. Calculate the own price & income elasticities of demand for good Y. Interpret your computed values and say something about the type of good.4. Suppose the economy has 100 units each of goods X and Y and the utility functions of the (only) 2 individuals are: UA (XA,YA) = X0.25Y0.75, UB (XB,YB) = X0.75Y 0.25Show that pareto-improvement is possible if,…Assume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U= X2Y 2 , derive the Hicksian demand function for good Y.Suppose that i’s preferences over goods x and y are represented by the following utility function Ui(x, y)=x^0.8·y^0.2. Let m denote the consumer’s income, p denote the price of good x and let the price of good y equal 1. a) Find the Marshallian demand functions for goods x and y. b) Show how each of the demand function is affected by a change in the price of good x. c) Which of the goods is an inferior good?
- An individual has $12 dollars to spend on the two goods (y=12). The price of good #1 is $2 (p1=2) and the price of good #2 is $6 (p2=6). How much of good #1 will the individual demand and how much of good #2 will the individual demand if their utility function is given by the following expression: U (q1 , q2) = q1 +2q2 a.) Quantity demanded of good #1 = b.) Quantity demanded of good #2 =Suppose U = 2X + Y, I = 20, Px = 2, and Py = 2. (a) Find Marshallian demand for X and Y . (b) What is Marshallian demand for X and Y if the price of X increases to 5? How much of the change in demand for X is the income effect and how much is the substitution effect? (c) How much is compensating variation for the price change described in part (b)? (d) How much is equivalent variation for the price change described in part (b)? ( Please solve all the subparts ASAP I will give you thumbs up . )The market for cellular phones has seen a combination of improving telecommunication technology and rising consumer incomes. Suppose you are told that the price of cellular phones decreased over the past five years. The decreasing prices of cellular phones, a normal good, implies that the magnitude of: A. he rightward shift of the demand curve is greater than that of the rightward shift of the supply curve B. The leftward shift of the demand curve is greater than that of the rightward shift of the supply curve C. The rightward shift of the demand curve is less than that of the rightward shift of the supply curve D. The rightward shift of the demand curve is less than that of the leftward shift of the supply curve
- Suppose that we can represent Joyce's preferences for cans of pop (the x-good) and pizza slices (y-good) with the utility function min[4x,5y]. a) Find her Marshallian Demand Functions. b) Find her Hicksian Demand FunctionsSuppose your utility for goods x1 and x2 is represented by the following utility function: U(x1,x2)= x11/5 x24/5 a) What is your marginal rate of substitution, MRS12? b) If the price for good x1 is p1 = 2, the price for good x2 is p2 = 4, and your available income is m = 20, write down your budget constraint. c) Using the prices and income given at b) above, find your optimal consumption choice bundle (Marshallian demand) and its corresponding utility level. d) Illustrate your optimal consumption choice on a graph. e) For the prices given in b), what income would you need to achieve a utility level of 25? PLEASE ONLY ANSWER PART C, D AND ESuppose your utility for goods x1 and x2 is represented by the following utility function: U(x1,x2)= x11/5 x24/5 a) What is your marginal rate of substitution, MRS12? b) If the price for good x1 is p1 = 2, the price for good x2 is p2 = 4, and your available income is m = 20, write down your budget constraint. c) Using the prices and income given at b) above, find your optimal consumption choice bundle (Marshallian demand) and its corresponding utility level. d) Illustrate your optimal consumption choice on a graph. e) For the prices given in b), what income would you need to achieve a utility level of 25?
- Now, imagine that instead of the subsidy the UK government had responded to the cost-of-living crisis by subsidising both energy and food demand through a subsidy to producers resulting in a reduction of both energy prices and food prices by 10%. Using the same indifference curve of point a., what is the optimal level of consumption of energy following such intervention? How much of the change in quantity of each good consumed is due to an income effect and how much to a substitution effect? please could you answer this showing a diagram of the indifference curve movement. could you do food on the y axis and energy on the x axis.Suppose a consumer in a competitive market maximises utility subject to a standard budget constraint. a. Given their resulting demand function, what assumptions would be required for one to conclude that when the price of good 1 goes up the consumer buys less of that good?b. Given their resulting demand function, what assumptions would be required for us to conclude that when the price of good 1 goes up the consumer buys more of good 2?The utility function of a certain consumer is U =(x1,x2)= x11/3 x22/3 , x 1and x 2 is the consumption of two kinds of goods, and the consumer's income is 100. The current prices of the two kinds of goods are P 1 =1 and P 2=2 respectively, ask: 1. If the price of the first commodity increases from 1 to 2, and other factors remain unchanged, what is the total effect of the price increase on the consumption of the first commodity? According to the Slutsky decomposition principle, what are the income effect and substitution effect? 2. Calculate the amount of income compensation that changes the price of the first commodity from 1 to 2, keeping the original effect unchanged