Suppose we have the following utility function: U(x,y)=x^0.33 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.

What is the marginal rate of substitution (MRS) for the utility function U(x, y) = x° + yP? The marginal rate of substitution of good x for good y is MRS = (Note: Be sure to use the Greek letter rho provided in the tool palette in your response.)

a) Explain by using an example why an MRS (Marginal Rate of Substitution) between two goods must equal the ratio of the price of the goods for the consumer to achieve maximum satisfaction?

3. The utility that Elena receives by consuming food F and clothing C is given by U(F, C) = FC + F. Food costs £1 per unit, and clothing costs £2 per unit. Elena's income is £22. MUF = C+1 and MUc = F. (i) Define the term Marginal Rate of Substitution (MRS) (ii) Find the utility maximizing values of C and F for the numerical values given above (Hint: You can assume interior solution). (iii) Now suppose that price of C and Elena's income remain unchanged at £2 per unit and £22, respectively, while the price of F varies. Find the equation of the demand for F as a function of the unit price of F (PF).

For the Cobb-Douglas utility function: the income and substitution effects are necessarily the same size. there is only an income effect, no substitution effect. there is only a substitution effect, no income effect. the demand for each good is independent of changes in the price of the other good.

Diminishing marginal rate of substitution for a good means:     I. decreasing the quantity of a good that the consumer would give up for one more additional quantity of the other good     II. increasing the quantity of a good that the consumer would give up for one more additional quantity of the other good     III.   no change for the quantity of a good that the consumer would give up for one more additional quantity of the other good       IV. all answers are correct

Q.7 A consumer's utility function is given by the expression: U = (0.6A"' + 0.47'"s} Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases? Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate? Calculate the marginal rate of substitution of Y for X and interpret its economic meaning. Write the equation showing consumer's equilibrium condition. Obtain the equilibrium values of X and Y. Find the expressions for change in MUx due to increase in Y and change in MUy due to increase in X.

Can you help me answer this macroeconomics theory question

Consider the single-good utility function u(x) = 3x². du(x) a) Find the marginal utility of x, MUx = dx b) Plot the utility function and marginal utility function on two separate graphs. c) Does this utility function satisfy the law of diminishing marginal utility? Explain.

8. Fabian consumes X and Y and the following utility function represents his utility: U = 2XY a. With a utility function of U = 2XY, Fabian's MU, = 2Y and his MU, = 2x ,where MU is marginal utility. Write an equation for Fabian's marginal rate of substitution (MRS). b. Suppose Fabian's income is $120 and Px = S6 and Py-$2, where Px is the price of X and Py is the price of Y. Write an equation for Fabian's budget constraint. c. Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indifference curve: d. If Fabian is spending all of his income, how much X and how much Y will he choose? Use the equations you wrote in part's b and c to answer this question. e. What will Fabian's utility be with this combination of X and Y? f. Now suppose the price of X increases to P.=10. Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indifference curve. How will this change the optimal combination of X and Y? What…