Al Deardwarf also makes plastic deer for lawn ornaments. Al has found a way to automate the production process completely. He doesn’t use any labor–only wood and plastic. Al says he likes the business “because I need the doe.” Al’s production function is given by f(x1, x2) = (2x1 + x2)1/2, where x1 is the amount of plastic used, x2 is the amount of wood used, and f(x1, x2) is the number of deer produced.
(a) In the graph below, draw a production isoquant representing input combinations that will produce 4 deer. Draw another production isoquant representing input combinations that will produce 6 deer.
(b) Does this production function exhibit increasing, decreasing, or constant returns to scale?
(c) If Al faces factor prices (1, 1), what is the cheapest way for him to produce 4 deer? _______. How much does this cost? _______.
(d) At the factor prices (1, 1), what is the cheapest way to produce 6 deer? _______. How much does this cost? _______.
(e) At the factor prices (1, 1), the cost of producing y deer with this technology is c(1, 1, y) = _______.
(f) At the factor prices (3, 1), the cost of producing y deer with this technology is c(3, 1, y) = _______.