Chao's utility function is ♦ = 4��1/2 + ��2. She faces prices ��1 and ��2 and income (a) Write the Lagrangian for Chao's utility maximization problem. (b) Use the Lagrangian to solve for the optimal quantities of �1 and ��2 in terms of income and prices. (c) How much income must Chao have to consume both goods?

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A consumer has the following utility function: Ulx, y) = xy -y, *21 where x and y represents the quantities consumed of goods X and Y. y 20 What will be the substitution and income effects for X and Yassuming that the consumer attempts to maintain the same level of utility achieved before price of Y increased (that is, when price of Y was $1)? SEx= +0.5 IEx = -0.5 SE, = -0.25 IE- = -0.25 SEx= +0.293 IE = -0.293 SEy = -0.414 IE, = +0.414 SEr= +0.25 IE SE, = -0.75 IE, = -0.75 = -0.25 SEx= +0.414 IEx = -0.414 SEy = -0.293 IE, = -0.207 Income = $3 Px= $1, Py= $2

Answer  typed .

Assume Pat spends all of her allowance to purchase 4 apples and 4 candy bars. Pat's marginal utility of the fourth apple is 20 utils, and her marginal utility of the fourth candy bar is 40 utils. If an apple costs $1.00 and a candy bar $0.50, to maximize utility Pat should(A) purchase more apples and more candy bars(B) maintain the current purchase of 4 apples and 4 candy bars(C) purchase more apples and fewer candy bars(D) purchase fewer apples and more candy bars(E) purchase fewer apples and fewer candy bars

4. Consider the utility function U(r,g) r + Iny. (a) Find the marginal rate of substitution. MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of r and y. How do you interpret these functions? How might a consumer choose between e and y as she tries to increase utility by, for example, consuming more when their income increases?

An individual’s utility function is given byU = x1√x2where x1 and x2 denote the monthly consumption of two goods. Unit prices of these goodsare $2 and $4 respectively, and the total monthly expenditure on these goods is $300.(a) Write down the budgetary constraint.(b) Find the optimal quantities of x1 and x2 the maximize U.(c) Verify that the stationary point is a maximum.

12. What are the mathematical steps in deriving demand and indirect utility?

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A consumer’s preferences between goods x and y are representedby the utility function u(x, y) = 2min{x, y}+10. Suppose this consumer hasincome of $16, the price of good x is $3 and the price of good y is $1. Suppose the price of good x increases to $7 while the price of good y andthe consumer’s income stay constant. Calculate the magnitudes of the compensating and the equivalent variations. Explain what each measures.