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[hotsim]

Can someone please solve these questions fro me. I've been banging my head all day. Thanks

Q.An individual utility function for two goods is given below: U = (x+2) (Y+1)
It is given that Px= Rs 4, Py= Rs 6 and the individual fixed income is Rs 130. Using the Lagrange multiplies method, find the optional levels of purchase of two commodities is the second- order conditions for maximum utility satisfied?

Q A Monopolist firm has the following total cost and demand functions:
C (x) = ax2+bx+c (a,b,c >o) and p (x) = B-  x (B>O)
Show that the firm’s optimum output level are equal when it fixes
a) Output
b) Price.

 

[JeffM]

Can someone please solve these questions fro me. I've been banging my head all day. Thanks

Q.An individual utility function for two goods is given below: U = (x+2) (Y+1)
It is given that Px= Rs 4, Py= Rs 6 and the individual fixed income is Rs 130. Using the Lagrange multiplies method, find the optional levels of purchase of two commodities is the second- order conditions for maximum utility satisfied?

Q A Monopolist firm has the following total cost and demand functions:
C (x) = ax2+bx+c (a,b,c >o) and p (x) = B-  x (B>O)
Show that the firm’s optimum output level are equal when it fixes
a) Output
b) Price.

First, we give help. not answers. We won't take the test; you will.

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OK about your first problem. Is it not obvious that, according to the model, there is no finite maximum for U? (To me that suggests that the model does not apply outside some undefined domain, but that limitation on the model is not relevant here.) But there is a maximum that can be spent, Rs 130. So we are dealing with constrained optimization. We need a finite answer.

In general, constrained maximization is dealt with in basic economics through a Lagrangian multiplier for each constraint.

In mathematical terms how would you define the constraint, given that you have two goods to spend income on?

How do you use that constraint to form a Lagrangian multiplier.