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Unformatted text preview: ECONOMICS 201
SPRING 2010 EXAM 2 instructions: Please mark your answers clearly. No ciass notes or other materials are allowed. 100 points total. Each question is worth
5 points with the exception of Q2, Q3, 012(15 points) and Q8‘ OH ([0 points). 1. Characterize the returns to scale (decreasing, constant. or increasing) associated with the following
production functions. (:3 a y=fu3X®Xn=ery+X3 a y=ﬁxpxp:mmpxﬁsxg 2. Dora the Explorer produces two outputs (output A and output B) using two inputs (input 1 and input 2).
The price of output A is PA , and the price of output B is PB. The price of input 1 is wI , and the price of input 2 is w2 . Dora produces output A using the production function yd = f A ( X l" , X 2" J , where Xf‘ is
the amount of input one and X; is the amount of input two allocated to output A. Analogousiy, she
produces output B using the production function y B : f 3 (X ,3 , X2B ) . (15 points) at What is Dora the Explorer’s PMP (proﬁt maximization problem)? b. What are the four ﬁrstorder conditions (with respect to X1”1 , X 2” , X13 , and X 2” )? MFA . MP3
0. Use the FOCs to show that MRTS of output A, {AA . ts equal to MRTS of output B, M}; B .
‘ 2 2 ,3 .3. Robert Woodruff produces Coke (output y) using one input, sugar (X). Coke is valued at price P in the
market, and the price ofsugar is w. His production function isy = f(X) = alnX , where or > 0. (Q po'nts) a. What is the PMP (proﬁt maximization problem)? b. What is the factor demand function, X (P, w) i? 0. Taking a partial derivative, show that the output of Coke increases when the market price of
Coke rises. A ﬁrm makes a product with the production function y = 2X 1 + 3X2. Input prices are wI = 1 and w2 : 2. What is the solution of the CMP (cost minimization problem) for 3—2 = [2 ? (Please circle one response.)
a. X] = 6. 11’: = 0 b. X1=0,X3=4
c. Xi=4,X3=O
d X,=3_.X3=2 A ﬁrm makes a product with the production function y = min{2XI ,3X2}. Input prices are wI :1 and w3 = 2 . “hat is the solution ofthe CMP (cost minimization problem) for y = 12 ? (Please circle one
response.)
a. X 6
b. X 4
0. X126,
d. X 0 Which of the following expressions is the average profit (Le. proﬁt per unit output)? (Please circle one response.)
a. AC MC
b. MCAVC
c. AVC—AC
d. MCAC
e. AVC—MC ...
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 Fall '08
 NINKOVIC
 Microeconomics

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