Question

2014 4. (a) Consider a monopolist who faces a market demand for his product: p(q) = 20 - 4, where p is the price and q is the quantity. He has a production function given by LK q = min 23) where L denotes labour and K denotes capital. There is a physical restriction on the availability of capital, that is, K. Let both wage rates (w) and rental rates (r) be equal to 1. Find the monopoloy equilibrium quantity and price when (i) when K = 24; (ii) K = 18. (12 marks] 2017 Question 20: A firm has the production function f(x,y)=x0.70 0.30. This firm has (a) Decreasing returns to scale and diminishing marginal product for factor X. (b) Increasing returns to scale and decreasing marginal product of factor x. (c) Constant returns to scale. (d) None of the other options are correct. Question 21: The production function is f(xx.xx)=x;"x". If the price of factor 1 is 8 and the price of factor 2 is 16, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? (a) X1 X2 (b) X=0.50 x (c) *1-2x2. (d) We can't tell without knowing the price of output.

Answer 1

eng a monopolist who faces a Total 2014 4ral considering a monopolist market demand for his product! P()= 20-9 Now, Morgan and reveme for the monopolist TRCZ) = pca).q = 209-92 Marginal revene of the monopolist! MRCa)= dCTR(2) - 20-29 . dq Now production function is given by". q= min 9 2 , & Now why. K = 24 .. Cequilibrium within find at a leve where amScanner

q q=h and I Now q = Ļ => 2=22 Now Cost function was ? Why war=1 will be e= WLtok = LAK K = 24 we out in .. substituting 2=² arting 2= 2q and 1 e=2q+24 Now Marginal cost M for the Condition Now Profit monimising a monopolist will be ? . monimising MR = mc 2) 20-22 =2 => 18-29 .=).q=9. and puce charged by monopolist, po 20-= (20-9) =$11 Huce, equilibrum quantity is quits and Om Price is $ 11, cs Scanned with CamScanner

also equilibrium will be al . K =18 When K= 18, then found where, q=Ļ - 2=22 tice here also cost Whis W =r=1 will be es Lt K. substituting L=2q and k-24 we quei . e=29124 Marginal cost me = 2 Now Piotit manimising Condition will be? MR = MC . 20-2q = 2 =) q= 9 . pull charged by monopolist.. P= 2029 20-q = (20 9) = $11 is q mits and equilibrium quantity pice is $11. Scanned with Cami Scanner

2017 Qustion 20 function's A firm has the the Production production Q=f(x,y) = 20.70 0.30 Now Q doubling both x and y We gut? F(2K, 24): 12 x 10.70 eye -2 20:4040.30 - 2Q hluce, doubling both to constand redus. enhibits function enhibits function Huce Production the Production to scale: thce the answu will ber ИМ Construct returns to scale. - Qusson 21% The production function f (21, 222) = 41% 42% Now, marginal product of ki 2 ..mpe Of (11)Ka] = txikimena axi - Marginal product of H2 (cs Scanne MP2 = 2F (**) 1 1/2 X 2/2 a R2 I with CamScanner

pull of Now factor 1, P,=8 and pure of ... condition is in factor 2, P2 = 16 Now optimal input min MPI. £ x 1-²242% I will ne ... . . XI x1= 2x2 =) Hace, the proportion that tim should use if it wants to manimise Profits will bei Les 21= 2x2 022 Scanned with CamScanner