PROBLEM SET - Problem 3 Given the expenditure function E =...

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PROBLEM SET Problem 1: A two product firm faces the following demand and cost functions: C= Q 1 2 +2Q 2 2 +10 Q 1 =40-2P 1 -P 2 & Q 2 =35-P 1 -P 2 a. Find the output levels that satisfy the first order condition for profit maximisation (Use fractions) b. Check the second order sufficient condition. Can you conclude that this problem possesses a unique absolute maximum? c. What is the maximal profit? Problem 2: Given the utility function U= lnX +2lnY and ‘price of commodity X’, P x =2, ‘price of commodity Y’, P y =3 and Income, B=18 i) Construct the budget line for the given problem. ii) Contruct the Lagrangian function and find the utility maximizing values of x and y iii) Find the maximum utility U * iv) Is the second order sufficient condition for maximum satisfied? v) What is the economic interpretation of the Lagrangian Multiplier?
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Unformatted text preview: Problem 3: Given the expenditure function E = 2X+ 3Y subject to the utility function lnX +2lnY=5 i) Contruct the Lagrangian function and find the expenditure miniimizing values of X and Y ii) Find the minimum expenditure E * iii) Is the second order sufficient condition for miniimum satisfied? Problem 4: Find ∫ (X+3)(X+1) 1/2 dx Problem 5: Verify that a constant c can be equivalently expressed as a definite integral. That is, show that C ≡ ∫ b ( c/b) dx Problem 6: Assume that the rate of investment is described by the function I(t) =12t 1/3 and that K(0)=25 a. Find the time path of capital stock K. b. Find the capital accumulation during the time intervals [0, 1] and [1, 3] respectively....
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