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?
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Suppose the function for the utility from good c is denoted as U(c)=2c1/2 . Which of the following expressions indicates the
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- 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.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 +XbThe 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?
- Assume that a person’s utility depends on two products, x and y. The utility function is given by U(x, y) = (x + 2)^2(y + 3)^3. Find the marginal utility of x and marginal utility of y.If the utility function of an individual takes the form: U = U ( x 1, x2) = (x1 + 2) 2 (x2 + 3) 3 Where U is total utility, and x1 and x2 are the quantities of two commoditiies consumed: (a) Find the marginal-utility function of each of the two commodities (b) Find the value of the marginal utility of the first commodity when 3 units of each commodity are consumed.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?
- You consume music (M) and concert tickets (C). Your utility function is U(M, C) = M1/4C3/4. The marginal utility for concert tickets, MUC is MUC =3/4C-1/2M1/4 and the marginal utility for music, MUM is MUm = 1/4C3/4M-3/4 (a) Calculate MRSMC using only the given marginal utilities. (b) Solve for the utility of bundle A where M = 16 and C = 16. Solve for your utility at bundle B where M = 128 and C = 8. Are the utilities the same? (c) Calculate MRSMC at bundle A and at bundle B. Are they the same? (d) Are your indifference curves convex? Draw the ICs. Make sure to label the quantities of the consumption bundles, the axis, and the MRS at those bundles.A utility function is given by the equation U = 20xe¬0.1x, where x is the number of glasses of wine consumed. (a) Show that this utility function has a maximum value and calculate the maximum utility. (b) Describe how marginal utility changes for glasses of wine consumed after the maximum utility is reached. Do you consider this reasonable? Give an explanation.Suppose we have the following utility function: U(x,y)=x^O.33 y^0.67 1) What is the Marginal utility of x? Marginal utility of y? 2) Comment on how the marginal utility of each changes as x increases and discuss why that makes sense. 3) Does this utility function follow the more is better rule? How do you know? 4) What is the marginal rate of substitution (MRS)? What do we know about the shape of the indifference curve given this MRS? 5) Now suppose we have a new utility function: U(x,y)=x+y. What type of goods are these? Explain.
- For each of the following utility functions, compute the marginal utility of good X (MUx) and the marginal utility of good Y (MUY). a. U(X,Y) = 3X1/2 + 5Y1/2 b. U(X,Y) = X0.5y0.4What kind of preferences are represented by a utility function of theform u(x1, x2) = √x1 + x2? What about the utility function v(x1, x2) =13x1 + 13x2?(Review Question) Sarah consumes both wine ) and cheese (y) and considers them perfect substitutes. She always gets twice as much utility from consuming wine as she does cheese. What equation would represent her utility function? U-(2xy) U=x+2y U=2x+y U=min(x,2y)
