Irma’s Handicrafts produces plastic deer for lawn ornaments. “It’s hard work,” says Irma, “but anything to make a buck.” Her production function is given by f(x1, x2) = (min{x1, 2x2})1/2, where x1 is the amount of plastic used, x2 is the amount of labor 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 5 deer.
(b) Does this production function exhibit increasing, decreasing, or constant returns to scale?
(c) If Irma faces factor prices (1, 1), what is the cheapest way for her to produce 4 deer? ______. How much does this cost? ______.
(d) At the factor prices (1, 1), what is the cheapest way to produce 5 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 (w1, w2), the cost of producing y deer with this technology is c(w1, w2, y) = ___________.