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2008midterm2answerkey

2008midterm2answerkey - Mid-Term ll Name 22452121214 ECO...

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Unformatted text preview: Mid-Term ll Name: 22452121214 % ECO 303 Spring 2008 ID: Multiple Choices(30pt) Idenafi the choice that best completes the statement or answers the question. M/Dk/ M/Z- / 1. Suppose over time that a firm’s production process incurs labor-saving M/K 7 M/L technological progress. This implies a a) the isoquants corresponding to any particular level of output will shift inward , WI: toward the origin and the MRTSL K along any ray from the origin will' 1ncrease. & b M/L 7 M /< ) the isoquants corresponding to any particular level of output will shift outward from the origin and the MRTSL, K along any ray from the origin will decrease =? MK 73' ,p/fl/‘S/ the isoquants corresponding to any particular level of output will shift inward toward the origin and the MRTSL K along any ray from the origin will decrease. d) the isoquants corresponding to any particular level of output will shift outward from the origin and the MRTSL K along any ray from the origin will increase. 2. If the production function is Q=K+2L, then the elasticity of substitution is Dmer; ’— < 0 a) negative. //7l€fl/L, 3 4- .approaching infinity. c) zero. d) one. 3. With a Cobb-Douglas production function, the MRTSL K a) is undefined. b) implies upward-sloping, straight-line isoquants. c) remains constant as the firm substitutes labor for capital. . ”declines as the firm substitutes labor for capital. _, E {Q 4. Suppose the output elasticity of total cost is 2. This implies the average cost curve 0( L exhibits M C ‘——> = — :- a) increasing returns to scale. 2 )1’ C é ”7C .—: Z/f'C b) economies of scale. -9/}7C 7/4 C c neither economies nor diseconomies of scale. _ . . —) p. 6, S 0d15econom1es of scale. 5. Consider the production function Q=( L”: +K’”) . J’This production function exhibits 2 4); Jik‘b sz 1“] @$(7[_) :ékj :j: a) decreasing returns to scale. ,4 aonstant returns to scale. ~— "> (k 3+ 4 H/ c increasing returns to scale. (1) either decreasing or constant returns to scale, but more information is needed to determine which one. 6. isquant curve represents a) ll combinations of inputs in which the firm produces the same level of output. ”x— b) all combinations of inputs in which the firm has the same level of total cost. c) for a given level of output, the various points that will produce that same level of output at the same cost. d) Both a) and b) are true. True/False (30pt) , Indicate whether the statement is true or false. Explain why if your answer is false 7. l0. Minimum efficient scale is the highest level of output the firm can achieve. Fa/S’e/ fa #2 Whifi'mfl,’ The slope of the isocost line equals the ratio of the marginal productivities of the inputs. // (A? .- — . ’7- IZD‘C’ ”MFA m/K If average cost increases as output we have diseconomies of scale and decreasing return to scale. / ? ' 7%»: gAm/o/ 407% a» planar»: A high elasticity of substitution between capital and labor implies that labor demand will be more price elastic. T 11. In the short run, marginal cost can be measured as the tangent slope of the total cost curve plus the tangent slope of the short-run variable cost curve. F ad’rc a!“ affc .9er //”C:yf 2¢5t342+r47 12. Given a production function Q=F(K,L). When the price of K increases, to V produce the same amounts of output, the cost-minimizing quantity of K must decrease. - a F / {3C M Pfiévdfig’h 74117017371 (T Zen-772%, frpolayfic'm, W 74-2 the—mN/Aéw'y ZJHMV?’ lam/(II m 2* 6407/? , Questions(40pt) 13. Suppose a firm has a production function Q=2KL+L, a) what is the marginal rate of technical substitution (MRTS)? (3pt) k 7N Q \\ ll b) Does the firm have increasing return to scale? (3pt) c2”: >(ek)(>4)+»4 = oa/a H4 >4? = >(>k¢+4):¢£/.+>>4 CP/> 2/4? =? .Z/f’J‘ c) At first, the firm used 3 units of capital and 2 units of labor. Now, the firm wants to use only 1 unit of capital to produce the same amounts of output. What is thekelagicity of sgbsguulgon? (4pt) A (é) _, (9/ 0—9 / 44 T a, ) and ¢; L L amen“ [44 22!. +L -— 3 ”7/63 (54 _‘£. — g- : _. 2 fl : '2- £0 g .1 4—“..2: .2. 14. Suppose that a firm’s production function is given by QszKM. The price of labor (L), capital (K) and Material (M) are w=4, r=I, and m=1, respectively. a) If the firm wants to produce 324 units of output in the long run, what is the solution to the firm’s long run cost minimization problem (the optimal basket)? am ”1‘: _ mag _m/’m N ' /’ "fl M 9‘ = / = / k=2L , M:/< 92F; "(z/_)(2/.) :4Léfi b) If the firm wants to produce 324 units of output, what is the solution to the firm's shot run cost minimization problem when M=4 (the optimal basket)? (5pt) , ?>}‘=4‘4 k /_= 5/? 8/:4’k — )M :zL f]: 3L3 fl 3L3 2 4 15. Suppose that a firm’s production function is given by Q = min (L, 2K), w = $10 and r = $5. If the firm wants to produce 1,000 units of output, a) What is the most efficient combination of labor and capital (L, K)? (Spt) [.r—lwv >k=m>0 ? kw” =>>/<=z_ b) Suppose that the firm spends exactly $1200 in the most efficient way possible. How much outputs can the firm produce? (Spt) TC:J'k+/0 [__ IW=Ik+WK 9’ V?” :g k=¥g 443.2:fé 49=7é¢ 16. Suppose a firm’s short-run total cost curve can be expressed as TC(Q)=50Q2+12Q+10. a) What is the fixed cost? (2pt) JFC = /o b) What is the average cost‘?(2pt) fiC': .454) +/z+—’q)i c) What is the average variable cost? (3pt) n 3 Art/c: @f/lfl :4—007‘42, d) What is the marginal cost? (3pt) NC 3 “-04? +/2 5 ...
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