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Running head: ECONOMICS Economics Name of the student Name of the university Author note
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ECONOMICS Answer 1 Initial price of three goods were Px= 1 PY=2 PZ= 3 the initial demand on he other hand was 500, 450 and 200. When the price of good X increases to 25 percent, the new price becomes 1.25 The new demand changes to xn, 465 and 190 a. therefore, the cross price elasticity Exywill be change the cross price elasticity will be % change in the demand of Y / % change in the price of X which will be 0.133 cross price elastocty of Exz will be -0.2 b The own price elasticity of demand is calculated by % change in the demand of X / % change the price of X Here, change in price of X is xn- 500 and change in price of X is 1.25 -1 Therefore, own price elasticity will be calculated asXn−500 1.25−1×1 500=Xn−500 125 Answer 2 a. q = -0.01L3+ L2+ 36L Where P = 0.10 and W = 4.80 MPL = dq/dl = - 0.03L2+ 2L + 36
ECONOMICS Now, MPL×P = W (- 0.03L2+ 2L + 36 ) 0.10 = 4.80 (- 0.03L2+ 2L + 36 ) = 48 L = 60 The firms demand for labour is 60 b. Total revenue will be price multiplied by the quantity which will be -0.01(60)3+602+36.60 = -2160 + 3600 + 2160 = 3600 Total cost will be 4.8*60= 288 Therefore profit will be TR – TC = 3600 -288 = 3312 Answer 3 a. solving the long run minimization problem 𝑦=l 1 3k2/3subject to TC = wl + rk ƛ wl + rk+ƛ [Y -l 1 3k2/3¿ dƛ / d k = r +ƛ2 / 3 k(2/3 -1)
ECONOMICS r +ƛ2/3 k(2/3 -1)= 0 r = - ƛ2/3 k(2/3 -1) ƛ= -3rk1/3 2l1/3 dƛ / d l = w + ƛ 1/3l 1 3−1 w + ƛ 1/3l 1 3−1= 0 w = -ƛ 1/3l 1 3−1 ƛ =3wl2/3 k2/3 wl2/3∗wl 2 3=k2/3*rk1/3 2wl = rk L= rk/ 2w Now, Y =l 1 3k2/3 Y =¿)1/3k2/3 Now, K =Y r/2w1/3 Therefore, Total cost will be wl + r.Y r/2w1/3 b.
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ECONOMICS c. total cost at k= 8 will bew×8r 2w+8r = 4r+ 8r = 12r d. average cost will be TC/ Y= wl+r.Y r/2w1/3 l 1 3k2/3 Average fixed cost Here fixed cost is rk or r Y/〖r/2w〗^(1/3) AFC = rY r/2w1/3 l 1 3k2/3 AVC = WL/l 1 3k2/3 e.
ECONOMICS the competitive firm will be producing as much quanity it wishes as long it accepts the prevailing market price. Since p is the price total revenue will be PY which is p.l 1 3k2/3 Answer 4 The cost function is C= 0.01𝑞3 − 1.2𝑞2 + 111q In perfect competition price is equal to the average cost Therefore the average cost will be AC= 0.01q2– 1.2q +11 Min AC dq/dc =0.02q-1.2 0.02q =1.2 q = 60 The firm’s output q is 60. b. Since Price is equal to Marginal cost and average cost in the long run, therefore for quantity 60 P = 0.01(60)2– 1.2(60) +111 Price is 75 Answer c 𝑄= 6000 − 20𝑝 Putting the value of P in the above equation, we get
ECONOMICS Q = 6000-20(75) Q = 6000 – 1500 = 4500 Since each firm is making 60 units, there must be 4500/60 which is 75 firms which are identically sized.