Eco 507 Midterm

ECO 507 Midterm Test 1. (i. ) ? =? lnQ/? lnP ? =P/Q* (? Q/? K) = Elasticity The coefficients of double put down model are the corresponding elasticities Price childs play = 1. 247 Income elasticity = 1. 905 (ii. )Price elasticity = -1. 2 Income elasticity = 2 Cross price elasticity = 1. 5 Current volume = 10 nautical mile Average income change magnitude by 2. 5% New qty after increase in income = Ie=2 2=%? Q%? I 2=%? Q/2. 5 %? Q=5% New Qty = 11. 445 mil To increase the sales volume only by 9. 2% you would shake up to reduce the price. %? Q/%? P=Pe -5. 25%?P=-1. 2 %? P=4. 375% (iii). a. maximiseZ = M + . 5S + . 5MS S? Subject 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 equivalence ? , I hit 1 + 0. 5S/60000 = 0. 5 + 0. 5M 2S M = 4. 5S By substituting into bud set down constraint, I get 30000S + 60000 * 4. 5S = 1200000 S = 4 M = 18 b. Cost function = 30000S + 60000M M arginal greet of S = 30000 Marginal cost of M = 60000 Total bare(a) cost = 90000 c. (iv. ) a. DemandQ = 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 Demand EquationQ = 2. 08 0. 2P 2. (i) Q = LK ?Q? L = K ?2Q? L2 = 0 The countenance order derivative did not give a negative value, so it ignores the condition of diminishing marginal productivity of labor. b. Q (L, K) = LK Q (mL, mK) = m? LK The output increases more than proportionally, there are increasing 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 equation, the firm should use K and L as given that balance to besmirch cost of production. The Lagrangean Multiplier is marginal cost of any stimulant drug to marginal benefit of any input should be same for any input. It explains if marginal cost benefit dimension is greater for K than L, we have to substitute L for K to minimize cost. d. 225 = LK 225 = 16L+144K L = 16L+144K + ? (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 daily rate above $60, there are x units vacant. So 60+X= 80-X 2X=20 X=10 If they cathexis 60+10=$70, 10 rooms will be vacant and 70- rooms will be occupied. The profit for 80 rooms clientele at $60 per room, TR= 80*60= $4800 TC= 4*80= $320 Profit = $4480 The profit for 70 rooms at the price of $70 TR= 70*70= $4900 TC= 4*70= $280 Profit= $4900 -$280= $4620 In this case the profit will also be maximized. 3. i) a) Maximize Y = 2Ty . 001Ty2 S. t. 100Ty + 25Tz = 1300 Also Maximize Z= 20 Tz . 1 Tz2 S. t 100Ty + 25Tz = 1300 b) I used the Lagrangean to get 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 Also 100Ty + 25Tz = 1300 Divide the first two equation to get 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 Wage rate = 12Now Q = 250 and so L required Then L* = 50 And Labor price is 12 so measure cost = 1250 = 600 500. You should not buy up the offer b) best amount of labor will be the one that equates MPL with wage ratio MPL = 10 0. 2L = 2 8 = 0. 2 L L* = 40 And wage paid = 80 This is the optimal point and I should accept the offer as 80 500 Profit = 500 80 = 420 iii) To calculate the optimal price I used the markup formula that says that P MC/ P = 1/ed Put the values to get P- 10/P = -1/1. 5 1. 5 P 15 = -P 2. 5 P = 15 P* = 6