Problem 1. Consider a production process that produces an output good, y, using two inputs, X1 and X2. We say that the production function f(x1,x2) exhibits constant returns to scale if for any real number t, f(tx1,tx2) = tf(x1,x2) If this holds with '=' replaced by < (or >), then f exhibits decreasing (or increasing) returns to scale. a) Explain why the 'perfect complement' and 'perfect substitute' production technologies we discussed in class (cf. Notes 14, slides 4-5) both exhibit constant returns to scale. b) Show mathematically that the Cobb Douglas production function f(x1,x2)=Ax19x2º can exhibit constant, decreasing, or increasing returns to scale depending on whether a+b>1.

Fig: 1