Constant Elasticity of Substitution utility function U(x. y) = (x^a*y^ (1-a))^b + y. I am looking for a this form of CES utility function to derive demand functions. (Note = > a is alfa, b is lambda).
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Constant Elasticity of Substitution utility function U(x. y) = (x^a*y^ (1-a))^b + y. I am looking for a this form of CES utility function to derive demand functions. (Note = > a is alfa, b is lambda).
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- . Economists often say that goods tend to have more elastic demand when they have lots of close χδ = α + (1 - a) substitutes. Use the CES utility function U(x, y) to show that the own-price elasticity of demand for good X gets larger (in absolute value) as the elasticity of substitution gets larger.What is the sum of the own price elasticity of demand for X, the cross price elasticities, and the income elasticity of demand for X? Does this hold only for the given type of utility function or all well behaved utility functions? What does this mean?If the utility function for a consumer is defined by U=6X^3/5Y^2/5 Given that the consumer's income is 300 currency units and unit price of goods X and Y are 12 and 15 currency units respectively, calculate the equilibrium quantity of both goods. Compute the price elasticity of demand for both goods and interpret your results. If income and prices of the two goods increase by 50%, calculate the equilibrium quantities of both goods
- a) A consumer has a utility function given by U = x025 y0.75 He has an income of £100, the price of good x is £5 and the price of good y is £10. How much of the 2 goods x and y does the consumer buy? Take a picture of your workings and upload with your answer, or type out your workings. b) For the utility function above, what is the cross-price elasticity of demand for good x with respect to the price of good y? Take a picture of your workings and upload with your answer, or type out your workings. c) For the utility function above, what is the elasticity of demand of good x with respect to its own price? Take a picture of your workings and upload with your answer, or type out your workings.Consumers view cake as an irreplaceable staple of any birthday party. Consumers also like to serve either cookies, ice cream, or donuts at birthday parties, but they don't need all three of those desserts as much as they need the cake. Assuming this is the only difference between these products, the price elasticity of demand for cake will be Response area the price elasticity of demand for ice cream. Is it greater than, less than, or equal too?You are given the following utility function (and there is obviously an income constraint). Derive the Marshallian demand function (half the points) and identify the income elasticity of both goods (half the points). u=x1x2
- Suppose the price of salt increases by 25 percent and, as a result, the quantity of pepper demanded (holding the price of pepper constant) increases by 3 percent. The cross-price elasticity of demand between salt and pepper is || (Enter your response rounded to two decim places and include a minus sign if appropriate.) In this example, salt and pepper are Instead, suppose salt and pepper were complements. If so, then the cross-price elasticity of demand between salt and pepper would be A. positive. B. negative. C. zero. D. greater than 1. E. less than – 1.Ralph consumes apples (A) and bananas (B). His Marshallian demand for bananas is 10.5 p0.2 6p0:7 B* = (a) Find and interpret the income elasticity of demand for bananas (eğ,1) and interpret the value. Are bananas an inferior or normal good? (b) Find the own price elasticity of demand for bananas (¤Â‚Ãß) and interpret the value. Does the own price elasticity of demand for bananas depend on the value of PB? (c) Find the cross price elasticity of demand for bananas (е‚Ã) and interpret the value. Are bananas and apples gross substitutes or gross complements?Suppose if the price of a good is $12, the quantity demanded is 50 units; when the price is $10, the quantity demanded is 100 units. Use the midpoint approach to compute the price elasticity of demand. Is demand at this point relatively responsive or relatively unresponsive to price changes?
- Consider a simple quasi-linear utility function of the form U(x, y) = x + In y. a. Calculate the income effect for each good. Also calculate the income elasticity of demand for each good. b. Calculate the substitution effect for each good. Also calculate the compensated own-price elasticity of demand for each good. c. Show that the Slutsky equation applies to this function. d. Show that the elasticity form of the Slutsky equation also applies to this function. Describe any special features you observe. e. A modest generalization of this quasi-linear utility function is given by U(x, y) = x + f(y), where f' > 0, f" < 0. How, if at all, would the results from parts a-d differ if this general function were used instead of In y in the utility function?Frank consumes only coffee. And his demand function given by Q = 12 − 2P where P is the price of coffee. What is the price of coffee when Frank has a unit elastic demand for coffee, that is, price elasticity of demand is equal to 1?Ravi's utility function for various combinations of X and Y satisfy all the axioms of choice. Given his budget constraint, it has also been observed that the cross-price elasticity of demand between X and Y is zero as the price of X falls. Given this scenario, comment with an appropriate diagram, what kind of commodity is Y?
