ps1_101_2011_1

# ps1_101_2011_1 - q boomerangs(i.e what is the ﬁrm’s...

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Economics 101 Problem Set 1 January 16, 2011 George J. Mailath Due Thursday, January 20, 2011 Please indicate your recitation time and recitation instructor on your answer. 1. The ﬁrm Oz Productions makes boomerangs. Its cost function is given by C ( q ) = 1 3 q 3 , where q is the quantity of boomerangs produced. (a) Calculate the ﬁrm’s supply curve (i.e., what is the proﬁt-maximizing choice of q as a function of the price of the good, q * ( p ))? (b) How does the proﬁt-maximizing quantity change in response to price changes, i.e., what is the slope of the supply function cal- culated in part 1(a) ? (c) Directly verify that this slope is also given by the formula dq * ( p ) dp = 1 C ±± ( q * ( p )) we derived in the ﬁrst lecture. 2. Suppose boomerangs are produced using a single input, labor, accord- ing to the production function q = f ( ± ) = (3 ± ) 1 / 3 , i.e., a quantity ± of labor will produce (3 ± ) 1 / 3 boomerangs. Suppose the price of labor is w . (a) How much labor is needed to produce q boomerangs? (b) How much does it cost the ﬁrm to produce

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Unformatted text preview: q boomerangs (i.e., what is the ﬁrm’s cost function)? (c) What is the proﬁt-maximizing choice of q as a function of the price of labor, q * ( w )? (d) How does the proﬁt-maximizing quantity change in response to changes in w ? (e) Directly verify that this change is also given by the formula dq * ( w ) dw = [ f ± ( f − 1 ( q * ( w )))] 2 wf ±± ( f − 1 ( q * ( w ))) we derived in the ﬁrst lecture. 1 3. Nicholson and Snyder problem 2.6. 4. Maximize the following: (a) 4 + x 1 − 3 x 2 − 3 x 1 x 2 − x 2 1 − 4 x 2 2 . (b) 4+ x 1 − 3 x 2 − 3 x 1 x 2 − x 2 1 − 4 x 2 2 subject to the constraint x 1 = 2 x 2 . (c) x 1 + x 2 subject to the constraint 1 x 1 + 2 x 2 = 2. (d) x 1 x 2 subject to x 1 + 3 x 2 = 4. (e) log x 1 + log x 2 subject to x 1 + 3 x 2 = 4. (Note that log is the natural log, i.e., base e ). (f) Is there a connection between your answer to parts 4(d) and 4(e) ? 2...
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ps1_101_2011_1 - q boomerangs(i.e what is the ﬁrm’s...

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