In footnote 7 we showed that, in order for a utility function for two goods to have a strictly diminishing MRS (that is, to be strictly quasi-concave), the following condition must hold: f2^2 f11-2 f1 f2 f12 f1^2 f22<0 Use this condition to check the convexity of the indifference curves for each of the utility functions in Problem 3.1 . Describe any shortcuts you discover in this process. | Numerade
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Hugo has a concave utility function of U(W)=W^0.5 . His only asset is shares in an Internet start-up company. Tomorrow he will learn the stock's value. He believes that it is worth 225 with probability 20 % and 256 with probability 80 % What is his expected utility? What risk premium would he pay to avoid bearing this risk? (Hint: See Solved Problem 17.2 .) | Numerade
Hugo has a concave utility function of U(W)=W^0.5 . His only asset is share…
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Consider a simple quasi-linear utility function of the form U(x, y)=x lny 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
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