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Unformatted text preview: we can replace into the constraint: ( Or ( ) ( , so that ( ) ) () ) and using the optimality condition we obtain () (b) Look at the last slides of Lecture 7. What is the total cost of achieving this level of output Q? Your answer should be a function of Q, w and r. ( ) ( ) ( ) () () (c) What if Q=30? What if Q= 40? Notice that now it only depends on w and r… ( ) ( ) (d) Suppose Q=30 and w=6 and r=24 , what are the demands for L and K? And the total cost? Now you should get an actual number. ( ) ( ) ( ) ( ) ( ) = 60*12=720 (e) Suppose that both labor and capital are twice as expensive as before. Do your demands for K and L change? Why do you think that’s the case? Do your costs go up? By exactly how much? ( ) ( ) ( ) ( ) ( ) 60*24=2 ( ) Do you remember the concept of homogeneity? So in this case, your demands seem to be homogeneous of what degree? And the Cost Function? The demands are homogeneous of degree zero: doubling the price of EVERY input does not change the optimal composition/mix of inputs, it just make...
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