A consumer has the following utility function ?(?, ?) = ?^0.2 ?^0.8 and Income=$800, Px =2,...

A consumer has the following utility function ?(?, ?) = ?^0.2 ?^0.8

and Income=$800, Px =2, Py =4
Note that ??? = 0.20 (y/x)^0.80 and ??? = 0.8 (x/y)^0.20

a) Find the initial equilibrium (x, y, U)
b) Assume that Px increases by 20% and Py decreases by the same percentage.

Find the new equilibrium (x, y, U).
c) Find the income and substitution effects of the above price changes.

Expert Solution

Rahul Sunny answered 1 year ago

a consumer has a utility function u = x^1/2y^1/2. prices are px = 2 and py...

a consumer has a utility function u = x^1/2y^1/2. prices are px = 2 and py = 3. she maximizes utility purchasing 6 units of good x. her income is equal to m = ________

Let assume that a consumer has a utility function u(x, y) = xy, and px =...

Let assume that a consumer has a utility function u(x, y) = xy, and px = 1 dollar, py = 2 dollars and budget=50. Derive the followings. (3 points each) 1) Marshallian demands of x and y 2) Hicksian demands of x and y 3) Indirect utility function 4) Expenditure function 5) Engel curve

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...

Suppose that a consumer has the following demand function: x ∗ (px, py, m) = 3mpy/px...

Suppose that a consumer has the following demand function: x ∗ (px, py, m) = 3mpy/px . What type of good is good x? (Remember, m > 0, px > 0, py > 0) (a) ordinary, complement, normal (b) ordinary, complement, inferior (c) inelastic, substitute, inferior (d) ordinary, substitute, normal

A consumer’s utility of income is given by the function ??(. ). The consumer has initial...

A consumer’s utility of income is given by the function ??(. ). The consumer has initial income $??, but risks losing $?? with probability ??. If a company offers insurance, the contract consists of coverage $?? at price $?? per dollar of coverage. (a) Using the notation above, what is the consumer’s expected utility with insurance? (b) Define actuarially fair insurance. What are the sufficient assumptions for insurance to be actuarially fair? (c) Prove that, if insurance is actuarially fair,...

Given Barbara's estimated Cobb-Douglas utility function, U(q 1, q 2) = q 1^0.2 q 2^0.8, for...

Given Barbara's estimated Cobb-Douglas utility function, U(q 1, q 2) = q 1^0.2 q 2^0.8, for CDs, q 1, and DVDs, q 2, derive her Engel curve for movie DVDs. Illustrate in a figure. Let p be the price of DVDs, $1.00 be the price of CDs, and Y be income. Barbara's Engel curve for movie DVDs is Y= ? (Please provide answer) (Properly format your expression using the tools in the palette. Hover over tools to see keyboard...

Consider a consumer with the utility function U(X, Y) = X^2 Y^2 . This consumer has...

Consider a consumer with the utility function U(X, Y) = X^2 Y^2 . This consumer has an income denoted by I which is devoted to goods X and Y. The prices of goods X and Y are denoted PX and PY. a. Find the consumer’s marginal utility of X (MUX) and marginal utility of Y (MUY). b. Find the consumer’s marginal rate of substitution (MRS). c. Derive the consumer's demand equations for both goods as functions of the variables PX,...

Suppose a consumer has a utility function u(x, y) = 2x + 3y. The consumer has...

Suppose a consumer has a utility function u(x, y) = 2x + 3y. The consumer has an income $40 and the price of x is $1 and the price of y is $2. Which bundle will the consumer choose to consume? Determine the demand functions for x and for y. Repeat the exercise if, instead, the consumer’s utility function is u(x, y) = min{x, 2y}.

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 .

Question