Question

In: Economics

Prove that that contract curve will be a straight line if the utility function for both...

Prove that that contract curve will be a straight line if the utility function for both consumers is U=3x²_iy_i

Solutions

Expert Solution

The pareto-optimal allocations would be where . For the consumer A, we have the utility as , and the marginal rate of substitution would be as or or or or or . It can be also found as , which would yield the same result.

For consumer B too, we have the same utility as , and the marginal rate of substitution would be as or or or or or .

The pareto-optimal allocation in this case would hence be where or or . The feasibility conditions are and or and , where and are the (given) endowments of A and B.

Putting this to the pareto-optimal condition, we have or or or or , which is the contract curve, and is an equation of straight line through the origin.

Rahul Sunny answered 7 months ago

Next > < Previous

Related Solutions

How can I prove that perfect substitutes utility function and perfect complements utility function are homothetic...

How can I prove that perfect substitutes utility function and perfect complements utility function are homothetic functions?

The position function of an object moving along a straight line is given by the function...

The position function of an object moving along a straight line is given by the function t3 - 15t2 -48t -10, where s is in metres and t is in seconds and 0≤15≤t . [7A] a) When is the velocity of the object greater than 21 m/s? b) When is the speed of the object less than 21 m/s? c) Illustrate the graphical representation for each of the above."

A basic feature of the utility function (demand curve) is the law of diminishing marginal utility....

A basic feature of the utility function (demand curve) is the law of diminishing marginal utility. That is, as a person consumes an item or a product, the satisfaction or utility that they derive from the product wanes as they consume more and more of that product. In other words, the price a person is willing to pay (or the demand) for that product decreases with consumption. However, our demand for some environmental goods (e.g., clean air/water) does not wane...

Prove that a Kempe’s mechanism traces an exact straight line using two identical mechanisms.

5. In the gizmo market, the supply curve is the typical upward-sloping straight line, and the...

5. In the gizmo market, the supply curve is the typical upward-sloping straight line, and the demand curve is the typical downward-sloping straight line. The equilibrium quantity in the gizmo market is 50,000 gizmos per month when there is no tax. Then a tax of $5 per gizmo is imposed. As a result, the government is able to raise $231,200 per month in tax revenue. We can conclude that the equilibrium quantity of gizmos has decreased by _______ gizmos per...

1.If a demand curve is a straight downward-sloping line, which of the following is true A....

1.If a demand curve is a straight downward-sloping line, which of the following is true A. The elasticity varies along the line B. The elasticity is constant along the line. C. The elasticity is inelastic along the line. D. The elasticity is perfectly elastic along the line. 2. The income elasticity for Good A is 0.7, and its cross elasticity with Good B is 0.7. What should we conclude about Good A? A. It is a normal good and a...

Determine the equation for the best straight line for the calibration curve from the following set...

Determine the equation for the best straight line for the calibration curve from the following set of absorbance/concentration (mg/100 mL) data: 0.96/0.0, 0.83/10, 0.66/20, 0.49/30, 0.36/40, 0, 19/50, 0.08/60. What method did you use to obtain the equation for the best straight line, what is the value of Ao, and what are the numerical value and units of k?

An object moves along a straight line. The position as a function of time is given...

An object moves along a straight line. The position as a function of time is given by the following 22 formula x(t)=5m+(2m/s)t–(0.6m/s)t^2. Please answer all of the parts, I will give a good rating**** :) How long after starting does it take the object to pass the origin? At what time is the object located 4 m from the origin? Sketch the following graphs: x(t), v(t), a(t). Find the object’s initial acceleration. At what time will the object come to...

Which of the following types of preferences and utility do NOT necessarily generate straight-line Engel curves?...

Which of the following types of preferences and utility do NOT necessarily generate straight-line Engel curves? Perfect substitutes Leontiev Cobb-Douglas Quasi-Linear A and C

A monopolist with a straight-line demand curve finds that it can sell 2 unit at 12...

A monopolist with a straight-line demand curve finds that it can sell 2 unit at 12 dollar each or 12 unit at 2 dollar each. Its marginal cost is constant at 3 dollar per unit. Draw the MR, and MC curves for this monoply

Subjects