The document describes a production function with capital (K) fixed at K0 and varying labor (L) from 0 to 5. It asks to: (1) calculate total, marginal, and average product with α = 0.5; (2) determine if returns to scale are constant, increasing, or decreasing with α = 0.5; (3) determine returns to scale with α = 1; and (4) calculate α if returns are constant and K = L = 1 initially with output = 0.2.

1. Consider q is output level, K is capital input and L is labour input. In the short run, capital input is
fixed at K0. Labour input varies from 0 to 5 . Production function is given by q=KL. (a) Suppose ==
0.5. Calculate the short-run outputs when labour input is 0 , 1,2,3,4, and 5 respectively. Calculate
the total product and then use the total product values to calculate the marginal product and
average product. Indicate whether or not marginal product is diminishing. (b) Suppose ==0.5.
Does this production function exhibit constant, increasing or decreasing returns to scale? Using
the definition of returns to scale to explain. (c) Suppose ==1. Does this production function exhibit
constant, increasing or decreasing returns to scale? Using the definition of returns to scale to
explain. (d) Initially, L=K=1. If the production function exhibits constant returns to scale, and =0.2,
what is the value of ?