Question

The production function is f(0, ,32) = 00112 062th The price of factor I is 212 and the price of factor 2 is 224 Ral a In what per proportions should the firm uses factors I and 2 if it wants to maximise profits ? b) show that the nom Maximum profit is zero

Answer 1

Both questions have been solved below.

Given i da Let out production function be denoted by a 8 = free 12 = 2112 2112 let co, = Bice of factor 1 = £12 W = Bice of factor 2 = £24 a) We can show that for maximising protits, 1 the firm's isocost and isoquant Cuoves should be touching each other and not intersect. Here , c, I. are isocost cuoves with slope = - = -12 2 640 lapor We can also see that the isoquants q aq are such that g is tangent to q. The slope of the isoquant is given by MAS or the marginal rate of technical substitution MRTS," =- - MP 22

where MP ads Mpy do MP = 1 by ₂ MP = 1 (1) ² -MRTS = - 1 MRTS - - 2 . The slopes of the iso cost and isoquant cuores are equal at the point of tangency, MRTS = Slope of isecont I we can the firm amount as see that in order to maximise profits, should use factor 1 in twice the the other

6. let p = fice of free good that is bring I produced by the given from . Poolt A- PR-42- T = P2gth - 122 -24% 9 In order to maximise prolet, > 1200 - 3)2-2+=0 - " we have already alotaned 3 using this result, we get =) P=242 -p 52412 Substituting P = 2452 in the profit equation, we get X =2452 2/2 212 - 1221 - 240

T = 243 2,2 262 -1221 - 42 = 24 (2413 pas "2 - 12-20. ()) But i 2 ob we get x= x ( Dar et 12-04) - 21 (ats 12-12) 29 (24 -24) T=0 that the maximum Hence we have shown profit is zero