PS1 - x 2 1/3 subject to the following constraint x 1 2*x 2...

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UCLA Economics 11 – Fall 2010 Professor Mazzocco Problem Set 1 Due by October 7 before 9:00am in the box located outside room 2221E, Bunche Hall 1. Unconstrained Optimization (2 exogenous variables) Find the values of ( x , z ) that maximizes the expression y = 24x 1/4 z 1/4 – 3x – 3z 2. Unconstrained Optimization (1 exogenous variable) a. Find the value of x that maximizes y =500−(10−2 x ) 2 b. Make sure it is a maximum by checking the Second Order Conditions and plotting the function. 3. Constrained Optimization (2 exogenous variables) Find the values of ( x 1 , x 2 ) that maximizes the expression Y=x 1 2/3
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Unformatted text preview: x 2 1/3 subject to the following constraint: x 1 +2*x 2 = 600. 4. Partial Derivatives and Total Differential Suppose Q(r,s) = (1/4)ln(r) + (3/4)ln(s) a) Calculate ∂Q/∂r, ∂Q/∂s. b) Evaluate these partial derivatives at r=1/3, s=3 c) Write the total differential for Q d) Calculate dr/ds for dQ=0, that is, what is the implied trade-off between r and s holding Q constant. Use the result from the previous part. e) Show that Q=0 when r=1, s=1. 5. Constrained Optimization (2 exogenous variables) Suppose that F(x,y) = xy. Find the maximum value for F if we know x+y= K....
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