A consumer has the utility function of U(n,q,y) with a budget constraint of I = NQ? + y? _{y.} Use the Lagrangian Multiplier method to derive the demand functions.

A consumer has the utility function of U(n,q,y) with a budget constraint of I = NQ? + y? _{y.} Use the Lagrangian Multiplier method to derive the demand functions.

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## Related questions

Assume that an individual consumes two goods, X and Y. The total utility (assumed measurable) of each good is independent of the consumption rate of other goods.

The price of X and Y are respectively $40 and $60. Use the following table of total utilities to answer the following questions.

Good | Total utility X | Total utility Y |

1 | 20 | 45 |

2 | 38 | 78 |

3 | 54 | 108 |

4 | 68 | 135 |

5 | 80 | 159 |

6 | 90 | 180 |

a. The marginal utility of the fourth unit of Y is__________.

b. The marginal utility of the fifth unit of X is___________.

c. The marginal utility per dollar spent on the third unit of X is__________.

d. The marginal utility per dollar spent on the second unit of Y is__________.

e. If the consumer has $420 to spend, ______ unit of X and _______units of Y maximize utility subject to the budget constraint. Explain.

f. If the consumer has $220 to spend, _______ units of X and_______ units of Y maximize utility subject to the budget constraint. Explain.

g. If the consumer wanted 4 units of X and 6 units of Y, what would have to be his/her budget constraint in order to maximize his/her utility? Explain.