ECON 404 - Homework 1.pdf - Mia Ha ECON 404 Summer 2019...

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(a) (6 points) Suppose the cost function is given by T C (q) = F + cq where F; c > 0: At what output level is the average cost minimized? (6 points) Consider a monopoly market. Demand is given by Q(p) = 100 Mia Ha ECON 404 Summer Quarter 2019 Honewort 1 . - TC Cg ) = F t Cq ( F , c > O ) ACC g) = Ff t c . If we want to minimize the average eositgthen :O q has to be a really large number . q = to quantity Qcp ) = 100 p p = IN - g TR = 100g qd MRCq ) = too -2g MCC g) = MR (g) 10 = 100 - Iq g = 45 p = too -45=55 maximizing a = 45 maximizing I = 55 DWL = Ig x 45×45 = 1012 . 5 p ^ CS = ¥45 x 45 = 1012 'S too , yes 55 Hi . . . sa : : : :c :& : : : : : : : - ions : : MR l D = Its d 90 45 I
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(c) (6 points) Consider a monopoly market. Demand is given by Q(p) = 100 - p and the total cost function of the monopolist is TC(q) = 10q+800: If the government imposes the average cost pricing restriction, how much would the price and dead-weight loss be? Qlp )= 100 - p p = 100 - g TCC g) = log -1800 ACG ) = lot 8,01 Mug ) = 10 ACC g) = 100 - q to +891=100-9 8090-+9 - 90=0 gd - 90g -1800=0 { 9g to III. ' 00-10=90 IN 80=20 p n Quantity is 9=80 price is p = 20 AC DWL - - Lx 10×10=50 §¥w So the dead weight loss is 50 - i i 80190 Q 10
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Tel get g) = I 491 -192 ) & MC (g) = 91 -19£ Formarketti Qe Cp ) = 100 - Lp g , = 100 - Ip p = 50 - TRE p . q= 50g , - O . 599 Mrfq ) = 50 9 , Let MR , Cgt = McCoy 't 50 91 = 91 -192 50 - 2g , = q , 91=25-0.5927 From the calculation in market I 92=20-1*921 q , = 25 - 0.5 ( IO - ¥91 ) 9 , = 25 - IO t ¥9 , 91 = 15 + Eg 91 ¥91 = 15 q*_ Demand Elasticity for market : Hp (G) = . If = JO - = 25 / = - o ' ' ' ET , PY- = - 0.5 Inelastic ble - LL - 0.5 CO
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For . Market 2 : Q2 ( p ) = 50 - 0.5 p p = 5%92 = 100 - Iga TRL 92 ) = p.gg = 10092 - 2922 MR (g) = 100 - 492 MRC q ) = MC Cgs ) I 00 - 492 = 9 , t 92 100 - 9 , = 592 92=20-1*921 From the calculation on market 2 : 91=25-0.59292 = 20 - ¥ ( 25 -0.5g ) 92 = 20 - 5 + Is 92 92 = 5 t Es 92 ¥92 = 5 gI= Pat = 100 - 29£ = 100 - 2x = 2530 ¥-::i¥¥÷÷ = - I It's elastic because - I L - I
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Fix this one , tcfq ) - - 91 tccqg ) - 492 p= 10 - q Firmtthaxttecaf ) =p Castaway - Tccae ) = ( to - 91 - 92791 - 91 In-car ) 297 = 10-291 - ga - t O = g - 291-92 92=9-291 92 = 9 - 2×4=1 192=17 e- Firms : Mae takes )= play -19192 - Tccqa ) Iska ) CIO q - g) Cgs ) - 4qa 2£91 ) = to - ga . - Iga 4 292 0 = 6 - q , - Iqs 91=6 - 292 91=6 - 219 - Ige ) q , = 6 - 18 -149 , 391=12 191=47 -
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PL q ) = 100 - q , TC Cq ) = Iq Mc Cq ) = 2 p = I TR ( q ) = 100g - Iqd MRL g) = 100 49 profit It = TR ( q ) - TC ( q ) = 100g - Ig d - Iq Icq ) = 100 9 q = too - p = 100 - 2 = 98 It = p .
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