Economics 2150A/B Chapter Notes - Chapter 4: Lagrange Multiplier, Utility Maximization Problem, Budget Constraint

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coralporpoise546

19 Apr 2014

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Interior solution optimum bundle lies on b. c. Corner solution optimum bundle lies on a corner of b. c: optimization rule, at interior optimum, the slope of ic = slope of the budget constraint, mux/px = muy/py (interior solution only) At the optimum, the marginal utility of the last dollar spent on good x must equal the marginal utility of the last dollar spent on good y: solve for an interior solution. Two methods: tangency condition plus the budget constraint, lagrange multiplier method, identify a corner point solution, optimal consumption basket solves both a utility maximization problem and an expenditure minimization problem, applications of consumer theory : Understand future value, present value, and the marginal rate of time preference. Maximize utility subject to an income constraint. This chapter discusses the theory behind consumer decision-making. The consumer chooses how much of good x and how much of good y he/she can consume given their current income.

Related Questions

Characterize utility maximization. When consumers maximize utility,

A. they consume each good up to the point where the marginal utility per dollar spent is the same for each good.

B. the marginal rate of substitution equals the price of the good on the horizontal axis divided by the price of the good on the vertical axis at the point of optimization.

C. the slope of the indifference curve equals the slope of the budget constraint at the point of optimization.

D. all of the above.

harlequinrat418

budget line

marginal utility

complete property of preferences

market demand

consumption bundle

substitution effect

Giffen good

total effect

income effect

transitive property of preferences

indifference curves

utility

the marginal rate of substitution

utility function

1.	_____	The satisfaction or benefit that consumers receive from consuming goods or services.
2.	________________ _	A particular combination of specific quantities of goods or services
3.	________________ _	Consumers can rank all conceivable bundles of goods or services
4.	_____	If A is preferred to B, and B is preferred to C, then A is always preferred to C.
5.	_____	Equation showing a consumerâs perception of the total utility forthcoming from consuming each bundle of goods and services.
6.	_____	A set of consumption bundles each and every one of which provides a consumer with exactly the same level of total utility.
7.	_____	The number of units of Y that must be given up for total utility to remain the same when one more unit of X is consumed.
8.	_____	The addition to total utility attributable to consuming one more unit of a good, holding the consumption of all other goods constant.
9.	_____	The line showing all bundles of goods that can be purchased at given prices if the entire income is spent.
10.	_____	The change in the consumption of a good that would result if the consumer remained on the original indifference curve after the price of the good changes.
11.	_____	The change in consumption of goods results strictly from the change in purchasing power after the price of a good changes.
12.	________________ _	The sum of the substitution and income effects.
13.	_____	A good for which quantity demanded varies directly with price, causing an upward sloping demand curve.
14.	_____	A list of prices and the corresponding quantity consumers are willing and able to purchase at each price.

blushwildebeest943

Given prices for two goods PX = 2 and PY = 3 and a budget of $120 a consumer is trying to maximize the utility function U(X, Y ) = 2X0.3Y 0.7 . Use the Lagrange method to solve this problem, but donât worry about the second order conditions (if you wish, you can actually check that the MRS is decreasing and this utility function is well behaved). a) Write and solve the utility maximization problem subject to the budget constraint. What is the resulting value of the utility function? (U=49.0481) b) Write and solve the dual problem. Do you get the same optimal solution (the same optimal combination of X and Y)? What is the resulting expenditure? Does that match the budget of your original (primal) problem? (X=18, Y=28 should be the same as for a or very close due to rounding) c) Assume now general values for prices and income. Solve for the optimal amounts of X and Y as functions of PX, PY , and I. What conclusion can you draw regarding how you spend your budget when dealing with Cobb Douglas functions with exponents that add up to 1. You can actually try to solve the general case where we replace the exponents 0.3 and 0.7 with some Î± and Î², where Î± + Î² = 1. (Hint: you should find that you spend percent of your income on X and Î² percent of your income on Y. See if you can get there by solving!)

silverllama877

Economics 2150A/B Chapter Notes - Chapter 4: Lagrange Multiplier, Utility Maximization Problem, Budget Constraint

ECON 2150A/B Full Course Notes

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