Following the conventional notation, consider a representative consumer with the utility function ?(?,?)=??+? and the budget...

Following the conventional notation, consider a representative consumer with the utility function
?(?,?)=??+?
and the budget constraint ???+???≤?. Assume throughout that all prices and quantities are positive and infinitely divisible.

Derive the consumer’s indirect utility function ?(∙). Assuming initially that ??=??=1 and ?=10, calculate the change in the consumer’s utility if the price of good ? doubles, all else equal.

Solutions

Expert Solution

THE STEP BY STEP WORKING IS AS FOLLOWS-

FIRST WE DIFFERENTIATED THE U WITH RESPECT TO X AND Y AND THEN USING MRS WE FOUND A RELATION BETWEEN X AND Y

THEN WE SUBSTITUTED IT IN BUDGET CONSTRAINT AND FOUND OUR OPTIMAL X* Y* AND THEN WE DERIVED OUR INDIRECT UTILITY FUNCTION USING THEM AS MARKED IN THE BOXES.

THEN WITH THE VALUES GIVEN WE FOUND V1 AND V2 AND SUBTRACTED THEM FOR FINDING THE CHANGE .

HOPE IT WAS HELPFUL FOR YOU. PLEASE GIVE IT A LIKE. THANKYOU!

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

Consider a representative consumer with the utility function ?(?, ?) = ?? + ? and the...

Consider a representative consumer with the utility function ?(?, ?) = ?? + ? and the budget constraint ??? + ??? ≤ ?. Assume throughout that all prices and quantities are positive and infinitely divisible. Find the equation of an arbitrary indifference curve for this utility function (evaluated at ̅ utility level ?). Sketch of graph of this indifference curve (be sure to justify its shape and to derive/demark any points of intersection with the axes).

consider a representative consumer with the utility function ?(?, ?) = ?? + ? and the...

consider a representative consumer with the utility function ?(?, ?) = ?? + ? and the budget constraint ??? + ??? ≤ ?. Assume throughout that all prices and quantities are positive and infinitely divisible. Assume initially that ?? = ?? = 1 and ? = 10. Derive the consumers equilibrium cross-price elasticity between goods ? and ? and evaluate the value of this elasticity at the initial parameter values given .

Consider a representative consumer with the utility function ?(?, ?) = ?? + ? and the...

Consider a representative consumer with the utility function ?(?, ?) = ?? + ? and the budget constraint ??? + ??? ≤ ?. Assume throughout that all prices and quantities are positive and infinitely divisible. 1.a.Derive the consumer’s indirect utility function ?(∙). b.Then, derive the consumer’s expenditure function, e(∙), directly from ?(∙). c.Finally, derive the consumer’s Hicksian/compensated demand functions (denoted ? and ? , respectively) from e(∙). ?? 2.Assume initially that ?? = ?? = 1 and ? = 10....

Consider an economy where the representative consumer has a utility function u (C; L) over consumption...

Consider an economy where the representative consumer has a utility function u (C; L) over consumption C and leisure L. Assume preferences satisfy the standard properties we saw in class. The consumer has an endowment of H units of time that they allocate to leisure or labor. The consumer also receives dividends, D, from the representative Örm. The representative consumer provides labor, Ns, at wage rate w, and receives dividends D, from the representative Örm. The representative Örm has a...

Consider a consumer with the Utility function: U = C^1/5 O^ 4/5 and facing a budget...

Consider a consumer with the Utility function: U = C^1/5 O^ 4/5 and facing a budget constraint: M ≥ PcC +PoO Note: For this utility function MUC = (1/5)C^-4/5 O^ 4/5 and MUo = (4/5)C^1/5 O^ -1/5 Where C denotes the consumption of corn, and O denotes the consumption of other goods. A) For corn, characterize the income elasticity of demand, the price elasticity of demand, the cross price elasticity of demand and explain what each represents. (You do not...

Consider a consumer with the Utility function: U = C^1/5 O^ 4/5 and facing a budget...

Consider a consumer with the Utility function: U = C^1/5 O^ 4/5 and facing a budget constraint: M ≥ PcC +PoO Note: For this utility function MUC = (1/5)C^-4/5 O^ 4/5 and MUo = (4/5)C^1/5 O^ -1/5 Where C denotes the consumption of corn, and O denotes the consumption of other goods. A) Derive the Marshallian demand functions for C and O using the equilibrium conditions for an interior solution. B) Graph and fully label the Demand Curve for corn...

Tax on labor income - Consider a one-period economy where the representative consumer has a utility...

Tax on labor income - Consider a one-period economy where the representative consumer has a utility function u(C;L) over consumption C and leisure L. Assume preferences satisfy the standard properties we assumed in class. The consumer has an endowment of one unit of time. She earns the wage w per unit of labor supplied to the market and has wealth A which yields an interest rate r, so her income is partly coming from labor, partly from capital. Suppose that...

Consider the following utility function: U(x, y) = 10x + 2y. A consumer faces prices of...

Consider the following utility function: U(x, y) = 10x + 2y. A consumer faces prices of px = 1 and py = 2. Assuming that graphically good x is on the horizontal axis and good y is on the vertical axis, suppose the consumer chooses to consume 5 units of good x and 13 units of good y. What is the marginal rate of substitution (MRS) equal to?

Consider the following utility function: U = 100X0.10 Y 0.75. A consumer faces prices of Px...

Consider the following utility function: U = 100X0.10 Y 0.75. A consumer faces prices of Px = $5 and Py =$5. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 7 units of good X and 15 units of good Y. Then the marginal rate of substitution6 is equal to: MRS = . (Enter your response rounded to two decimal places. Do not forget to...

Consider the utility function of a consumer who obtains utility from consuming only two goods, ?1...

Consider the utility function of a consumer who obtains utility from consuming only two goods, ?1 and ?2 , in fixed proportions. Specifically, the utility of the consumer requires the consumption of two units of ?2 for each unit of ?1. i. Report the mathematical expression of the utility function of the consumer. ii. Provide a diagram of the corresponding indifference curves. iii. Provide at least one example and economic intuition. Suppose that the consumer has available income equal to...

Subjects