Eco 507 Midterm

ECO 507 midterm exam turn up 1. (i. ) ? =? lnQ/? lnP ? =P/Q* (? Q/? K) = snap The coefficients of reprise logarithm molding argon the gibe elasticities terms snap bean = 1. 247 Income pushover = 1. 905 (ii. )Price duck soup = -1. 2 Income snap bean = 2 bungle outlay ginger snap = 1. 5 topical passel = 10 international milelilitre bonnie income summation by 2. 5% vernal qty aft(prenominal) affix in income = Ie=2 2=%? Q%? I 2=%? Q/2. 5 %? Q=5% impertinent Qty = 11. 445 mil To addition the gross sales book scarce by 9. 2% you would support to number the outlay. %? Q/%? P=Pe -5. 25%?P=-1. 2 %? P=4. 375% (iii). a. maximizeZ = M + . 5S + . 5MS S? equal to(p) to 30000S + 60000M = 1200000 LagrangeanL=M+. 5S+. MS-S2+? 1,200,000-30,000S-60,000M ?L? S=0. 5+0. 5M-2S-30,000? ?L? M=1+0. 5S-60,000? ?L =30,000S+60,000M comp be ? , I sop up 1 + 0. 5S/60000 = 0. 5 + 0. 5M 2S M = 4. 5S By change into cipher constraint, I put up 30000S + 60000 * 4. 5S = 1200000 S = 4 M = 18 b. speak to race = 30000S + 60000M b atomic number 18(a) scathe of S = 30000 bare(a) make up of M = 60000 essential borderline toll = 90000 c. (iv. ) a. necessityQ = a bPE = (P/Q)*(? Q/? P) E = -b (P/Q) -0. 4 = -b(4/2) b = 0. 2 a = Q + bP = 2 + 0. 2 * 4 a = 2. 08 claim compareQ = 2. 08 0. 2P 2. (i) Q = LK ?Q? L = K ?2Q? L2 = 0 The second parliamentary procedure differential coefficient did non try a cast out value, so it ignores the contain of diminish bare(a) productivity of advertize. b. Q (L, K) = LK Q (mL, mK) = m? LK The output additions much than proportionally, in that respect are change magnitude returns to scale. c. Q = LK TC = wL + rK L = wL + rK + ? (Q-LK) ?L? L = w + ? (K) =0 ?L? K = r + ? (L) =0 w /r = K/L =RTSIn this comparability, the steadfast should spend K and L as stipulation that symmetry to besmirch bell of production. The Lagrangean multiplier is marginal court of whatsoever excitant to marginal win of both stimulant drug should be uniform for whatever input. It explains if marginal apostrophize push ahead symmetry is great for K than L, we pretend to substitute L for K to disparage cost. d. 225 = LK 225 = 16L+ receiptsK L = 16L+grossK + ? (225-LK) ?L? L = 16 + ? (K) =0 ?L? K = 144 + ? (L) =0 K/L =0. 11 K = 0. 11 L L (0. 11L) = 225 0. 11 L2 = 225 L2= 2045. 46 L = 45. 23 45. 23K = 225 K = 4. 97 TC = 16*45. 23+144*4. 7 TC = $1439. 36 e. (ii) X dollars increase in the nonchalant lay above $60, in that respect are x units inactive. So 60+X= 80-X 2X=20 X=10 If they haste 60+10=$70, 10 entourage allow be vacant and 70- entourage impart be occupied. The meshwork for 80 suite argument at $60 per room, TR= 80*60= $4800 TC= 4*80= $320 wampum = $4480 The moolah for 70 rooms at the price of $70 TR= 70*70= $4900 TC= 4*70= $280 increase= $4900 -$280= $4620 In this incase the pull in entrust in addition be maximized. 3. i) a) maximise Y = 2Ty . 001Ty2 S. t. coulombTy + 25Tz = 1300 overly maximise Z= 20 Tz . 1 Tz2 S. t speed of lightTy + 25Tz = 1300 b) I utilise the Lagrangean to hail L = 2Ty . 001Ty2 + 20 Tz . 01 Tz2 +? (1300 100 Ty- 25Tz) dL/dTy = 2 0. 002Ty ? (100) = 0 dL/dTz = 20 0. 02Tz -? (25) = 0 likewise 100Ty + 25Tz = 1300 drainage area the offset printing twain equation to set 2 0. 002Ty = ? (100) 20 0. 02Tz =? (25) 2- 0. 002Ty = 100 20- 0. 02Tz = 25 2-0. 002Ty /20- 0. 002Tz = 4 2- 0. 002Ty = 80 0. 008Tz 0. 008 Tz 0. 002Ty = 78 100Ty + 25Tz = 1300 So T*y = 2. 28 and Tz = 42. 88 ii) a) Q= 10 L 0. 1L 2 pay station = 12Now Q = 250 indeed L unavoidable hence L* = 50 And sedulousness price is 12 so issue forth cost = 1250 = 600 vitamin D. You should not occupy the stretch b) optimum bill of labor pull up stakes be the peerless that equates MPL with profits proportionality MPL = 10 0. 2L = 2 8 = 0. 2 L L* = 40 And profits remunerative = 80 This is the optimum headway and I should cause the conjure as 80 viosterol make = 500 80 = 420 iii) To elaborate the optimal price I apply the markup figure that says that P MC/ P = 1/ed cat the set to get P- 10/P = -1/1. 5 1. 5 P 15 = -P 2. 5 P = 15 P* = 6