6-4.6 a. See figure. b. See figure. Assume the number of copy machines is fixed at 1. Then production K function is  1000 * min(L, 3). For  3,  1000L; for  3,  3000. Q L Q L Q 6-5.3 a. This production always displays constant return to scale. b. The Cobb- production function has decreasing, constant, or increasing returns to scale as is less than, equal to, or greater than 1.    c. This production function has decreasing, constant, or increasing returns to as  is less than, equal to, or greater than 1.   d. The CES production function has decreasing, constant, or increasing returns to scale as is less than, equal to, or greater than 1. d 7-2.3 a. Variable cost is = 10q + VC(q) – bq2 q3. Average variable cost is = 10 + AVC(q) bq q2. – For this to be positive, 10 + > 0 bq q2 – 10 + > q2 bq < 10/q + b q, b. The average cost curve is U-shaped. is minimized at 2q  Fq2    AC dAC/dq b 0. c. crosses when the functions are equal. where 10 2bq 3q2 MC AC MC  AC    F/q 10 where 10 2bq 3q2 10   bq  q2. MC  AVC     bq  q2. d. is minimized where 0.  AVC dAVC/dq 2q 0    dAVC/dq b – or  2q b  MC AVC where 10 2bq 3q2 10      bq q2.
6-4.6 a. See figure. b. See figure. Assume the number of copy machines K is fixed at 1. Then production function is Q  1000 * min(L, 3). For L  3, Q  1000L; for L  3, Q  3000. 6-5.3 a. This production always displays constant return to scale. b. The Cobb- production function has decreasing, constant, or increasing returns to scale as    is less than, equal to, or greater than 1. c. This production function has decreasing, constant, or increasing returns to as    is less than, equal to, or greater than 1. d. The CES production function has decreasing, constant, or increasing returns to scale as d is less than, equal to, or greater than 1. 7-2.3 a. Variable cost is VC(q) = 10q – bq2 + q3. Average variable cost is AVC(q) = 10 – bq + q2. For this to be positive, 10 – bq + q2 > 0 10 + q2 > bq b < 10/q + q, b. The average cost curve is U-shaped. AC is minimized at dAC/dq  Fq2  b  2q  0. c. MC crosses AC when the functions are equal. MC  AC where 10  2bq  3q2  F/q  10  bq  q2. MC  AVC where 10  2bq  3q2  10  bq  q2. d. AVC is minimized where dAVC/dq  0. dAVC/dq  – b  2q  0 or b  2q MC  AVC where 10  2bq  3q2  10  bq  q2.
micro_homework_2.docx