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Maths for economics help!

I've got no idea where to even start with these questions! Please help! :smile:

Q1) A firm’s production functions is given by Q = AK^1/2L^1/4
If the prices of capital and labour are 100 and 10 per unit respectively,
evaluate the minimum cost combinations of the inputs given that the firm
produces 1000 units of output.

Q2) A consumer’s utility function is given by U=(x+2)(y+1)
The price of goods x and y are £4 per unit and £6 per unit respectively
and the consumer’s income is £130 per period.
(a) Write the Lagrangian function
(b) Find the optimal quantities of x and y
(c) Check the second order condition for a maximum.
Original post by CommonSenseLess
I've got no idea where to even start with these questions! Please help! :smile:

Q1) A firm’s production functions is given by Q = AK^1/2L^1/4
If the prices of capital and labour are 100 and 10 per unit respectively,
evaluate the minimum cost combinations of the inputs given that the firm
produces 1000 units of output.

Q2) A consumer’s utility function is given by U=(x+2)(y+1)
The price of goods x and y are £4 per unit and £6 per unit respectively
and the consumer’s income is £130 per period.
(a) Write the Lagrangian function
(b) Find the optimal quantities of x and y
(c) Check the second order condition for a maximum.


For 1) I'd start off with trying to minimise total costs = 100K+10L with the constraint of your output function being 1000. I think this would work if I haven't misinterpreted the question. Then solve this via the Lagrangian method.

For 2) you can form a budget constraint of 4x+6y=130 and then you can change your utility function into a Lagrangian and then take partials wrt each variable then solve simultaneously.
Thanks so much! I misinterpreted q1 but now it makes a lot more sense!:smile:

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