In Using Lagrange Multipliers to Minimize the Function $f ( x , y ) = x ^ { 2 } + y ^ { 2 }$

question 169

Multiple Choice

In using Lagrange multipliers to minimize the function $f ( x , y ) = x ^ { 2 } + y ^ { 2 }$ subject to the constraint that $x + y = 3$ , what is the value of the multiplier $\lambda$ ?

• A) \(\frac { 1 } { 2 }\)
• B)1
• C) \(\frac { 3 } { 2 }\)
• D)2
• E) \(\frac { 5 } { 2 }\)
• F)3
• G) \(\frac { 7 } { 2 }\)
• H)4

---

Definitions:

APC

The acronym for Average Propensity to Consume, which measures the fraction of income that households spend on goods and services rather than saving.

Disposable Income

The cash pile households can utilize for their spending and savings needs after income taxes are handled.

MPC

Marginal Propensity to Consume, which represents the ratio of change in consumer spending to a change in household income.

MPS

The marginal propensity to save, which is the proportion of an increase in income that is saved rather than spent on consumption.