Question

A firm has the production function f(x, y) = min[2x, x + 2y). On the graph below, use the line tool to draw the production isoquant for this firm where f(x, y) = 10. Make sure your isoquant extends to the edges of the graph. To refer to the graphing tutorial for this question type, please click here. Production Isoquant

Answer 1

x and y are perfect complements of each other. The production function is Leontief i.e. Fixed Proportion. So, the isoquant will be L shaped wth a kink as shown in the below diagram. Also, Marginal Rate of Technical Substitution is not defined at kink points as the isoquants are not continuous.

f(x, y) = Min (2x, x+2y) It is given that, f(x,y) = 10 Case 1 If 2x > &+@y » x>2y then, flowy) = x+2y = 10 Cape 2 If 2x < x + 2y x < 2y then, f(x, y) = 2x = 10 Finding relation in terms of y for Cape 1: xay y < x 0 , f(x,y)= x+2y for cape 2 - acay y > 2 -- , f(x,y) = 2x f you - y = x/ for yc a for y a Isoquants are perfect substitutes Isoquants are vertical line f(x) = 2x-10.