Question

9.1 Power Goat Lawn Company uses two sizes of mowers to cut lawns. The smaller mowers have a 24-inch blade and are used on lawns with many trees and obstacles. The larger mowers are exactly twice as big as the smaller mowers and are used on open lawns where maneuverability is not so difficult. The two production functions available to Power Goat are: Output per Hour (square feet) 8000 Capital Input (# of 24" mowers) Labor Input Large mowers Small mowers 5000 a. Graph the g = 40,000 square feet isoquant for the first production function. How much kand/ would be used if these factors were combined without waste?

Answer 1

sol Given a poser Goof lawn company Labor input out put per hour capital input Large mowels fooo 5000 small mowers the labor are and the capital function co this production used the in tined proportion mathematical form of function fined proportions production q: min cake, be) alb so 621 5:1 Fora function for production q = 40,000 qsi 8000 K minivil) 1020 qi 600o y min lk, 112) - 8000 x 4 8000 x min (all) = Sooo yl = 40,000 l 40,000 food I= 2x5 Elo

Total capital requirement would be 10 units and labor requirement would be 5 q=40,000 3 Capital 9 h T 46 Flo • labor (²) The second production is function output 1 Labor input- palhr 1 capital input small mowers rooo Here cal, bil production function for a = 40,000 q = 5000 v min (kie) (nere kiel C 1000x min (kek) = 1000 XC - 5ooo x min (lil) soooxd q= 401000 Ki is 401000 5000 is Toll Capital Labor requirement . requirement- sunits Sunits