Şeyma has the following utility function: U(x,y) = x'/²y+/2 and faces the budget constraint: M = P,x + P,y. Suppose M = 120, P, = 1 and P = 4. Find the optimal x and y.
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- For each of the following utility functions get the marginal utility of consumption of each of the goods. 1/2 1/2 (a) u(a,b) = a b (b) u(x, y) = x³/4y1/4 (c) u(a, b) = n(a) + In(x) (d) u(x, y) = ln(x) + ln(y) (e) u(a, b) = 2xa +XbConsider the utility function u(x1, x2) = x10.5x20.5. Find the Marginal Utilities with respect to good x1 and x2.Suppose the function for the utility from good c is denoted as U(c)=2c2. Which of the following expressions indicates the marginal utility of c? 1/c2 1/square root of c All of the above are correct.
- Find marginal utility MU for a consumer consuming x amount of a given commodity, where his total utility function is TU = x²ln (x² + 1).3) Oğuz has the utility function U(x1,X2) = x:*x2². (X: nuts, X2: berries). %3D a) If Oğuz has 25 units of nuts and 17 units of berries, the price of nuts is 2 and the price of berries is 1 liras, what would be the optimal consumption of Oğuz? b) Assume the prices change, so that nuts cost 1 and berries cost 3 liras. What is the new demand? In this change, What is the pure substitution effect? What is the income effect? c) In the change calculated in part (b), what is the pure substitution effect? d) In the change calculated in part (b), what is the income effect? In the change calculated in part (b), what is the endowment effect?Suppose Paco has an annual entertainment budget of I. He spends his entertainment budget on only 2 goods: video games and movies. The price of a video game is P, and the price of a movie is Pm. Paco's utility function for video games (v) and movies (m) is: U(v, m) = 4v²m. a. Derive Paco's demand functions for video games and movies as functions of only exogenous variables. b. Write Paco's indirect utility function.
- The utility function of a certain good is given by U(x) = 60x - x2 where x represents the number of units produced and sold during a month.How many units must be produced and sold to maximize utility? What is the maximum utility?Biwei’s utility function U=4XY, where X is consumption of beer and Y is consumption of pizza. For this utility function, the marginal utility of X is MUx = 4Y; the marginal utility of Y is MUY = 4X. 1) Suppose Y = 3. Calculate Biwei’s utility for X = 2, 3, 10, and 11. For a given level of Y, does good X display diminishing marginal utility? 2) Suppose X = 3. Calculate Biwei’s utility for Y = 2, 3, 10, and 11. For a given level of X, does good Y display diminishing marginal utility?The utility of a consumer derives from consuming the two goods X and Y can be assumed to be determined by the utility functionU(X,Y)= 4X03Y05. If good X costs 10 birr a unit and good Y costs 15 birr a unit and the consumer's income is 120 birr. What combination of X and Y that will maximize utility?
- Suppose the function for the utility from good c is denoted as U(c)=2c1/2 . Which of the following expressions indicates the marginal utility of c?Suppose Al is currently consuming five movies and two concerts per month. If his utility function is given by U = 15MC, where Mrepresents the number of movies seen and C represents the number of concerts attended, Al's total utility is equal to: 75 15 150 10 30For the utility function U = Qx0.68Qy(1-0.68) and the budget 103 = 10Qx + 13Qy find the CHANGE in optimal consumption of Y if the price of X increases by a factor of 1.7.
