akmidterm105

# akmidterm105 - a X b min{w¥ rf 4pl 6 WIIZFHZ a er w...

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Unformatted text preview: a. X b. min{w¥, rf} 4pl 6' WIIZFHZ a. er w e. (min{wf,rf})n2 4pw '1 g. o Which of the above expressions could possibly be a: Proﬁt function? (4pm) Sc, Variable Cost function? (4pts) Coriational factor demand for labor? (4pts) 0‘\ Factor demand for labor? (4pts) :9ng 2. Show mathematically that the minimum of the average total cost curve occurs when the average total cost curve intersect the marginal cost curve. The formula for the average total cost curve is given by: ATC=(cV(x)+FC)/x. (6pts) M ; q CM (a) + PC X X £_ “'3 O T “" Cuba) tFC )6 x x2 :7 Cu (in) +FL d Cu in) TC XL 1 “ii, \) X a. co mch _ A Cu 05) C/ Me ' W 3. A ﬁnn’s production function is given by: x=LmK2/3. Find the ﬁrm’s factor demands. (6pts) A‘ P :33 9-foka 90 L200 van Bob and Larry have identical preferences over cucumbers (x) and tomatoes (y): UB=UL:2X”2 +y and are stranded on a desert island. Bob is endowed with 15 cucumbers and 0 tomatoes. Larry is endowed with 3 cucumbers and 6 tomatoes. a. Draw an Edgeworth box that represents their current endowments. Be sure to label all relevant points. (2pts) b. Sketch some ‘nonnal’ indifference curves for Bob and Larry through the endowment point. Show where trades between Bob and Larry could happen. Within this set, show a place where no more trading could happen (Le. a Pareto efﬁcient point) and sketch the indifference curves through this point. (2pts) c. Derive Bob and Larry’s Marshallian demands as functions of the p;, py, and their endowments. (opts) d. Calculate the market clearing prices. (4pts) e. Does Bob achieve a higher utility level than Larry after trading? (2pts) HC‘ 1: 11814.); +A<px£+yjﬁ*pix'%9) 37" 44, ., ,. (QB—7: "“ l?“ leX'0 mgrg ’1— "APS to % .4\:_#:P3 0‘6 / ON 3"“th 1M fag‘j NH (\3 _/‘7 away?" : ﬁg Pa 1 X 1 5’3 P) .5 .1 H A 93) \jr'; ()XergbLj-V :hplx4_jﬂpﬁ 9 07 E 3 Xetyb' .3. I Vx ‘2 ‘39» ’ '6; ‘6 '- 83 Pa PX 5M a @r‘\&€f3 claw m vn a»ka £1or‘ )L a 1 £1 a ( Fx ' ‘3 (DA :: 3 9y AM- u A F! ’g/ )po‘h ¢onsun~L 3L,”st Q Bug Lu, 0 I "sf—LUV Vikki. chv/ by,” 1 buy)” “€- j 1/ v) 32% \{ wah c413 ﬂ Mfg h CL- C. :5 S. Laura’s indirect utility function is given by: v(pl‘,, p]. , M) = a. b. C. §0\VL a, 4M' pip}- Find Laura’s expenditure function. (2pts) Find Laura’s Hicksian demands. (4pts) Suppose that p" and py were both 1 and that Laura reached a utility level of 64. How much money did Laura have? How much x and y did she consume? (3pts) Suppose now that px increased from 1 to 4. How much x and 3/ does she consume now? Break out her changes into income and substitution effects. (6pts) Suppose Laura decided to bribe the owner of the company producing x to not raise their price. What is the largest bribe she would be willing to pay? (4pts) Cow e/L \) '2 D‘ Kktlzl; E OF (9L0 : L ‘jktli 519‘th lesMﬂ‘M Junior’s ﬁrm needs to produce 100 units of x. His production function is given by x=min{L1+2L2,K} where L1 is one type of labor and L2 is another type of labor. The price of L1 type labor is W1 and the price of L2 type labor is W: a. Derive J unior’s conditional factor demands for L1, L2, and K. (6pts) b. Derive Junior’s variable cost function. (2pts) c. Calculate Junior’s conditional factor demands for L1, L2, and K when w1=l, wz=3, and 1:12. What are his total costs? (2pts) d. Suppose it is mandated that wages are the same for the two types of labor increasing W] from 1 to 3. How do Junior’s conditional factor demands for L1, L2, and K change? (2pts) [1‘ Ma 1L7, h LO‘ < W_2_ L r )4 x: 2_ 19 " n. wt [/1L 3 \$1: ‘C— “3' Z '72: 0 l9. (,(N‘JWLJVJ \$23: r; 4r wail/V3)”ng 2 Lu, 3 0 L091 m 6‘} +an t i’uvo T \300 ...
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