Economics Production and Cost Theory: Solved Problems

Posted on Apr 5, 2025 in Economics

Economics: Production and Cost Theory – Solved Problems

Production and Cost Theory Problems

  1. c. The company produces at the technical optimum.
  2. d. It should choose 1,500 units of labor and 7,500 units of capital.
  3. a. Straight lines with a negative slope.
  4. a. Decreasing returns to scale and diseconomies of scale.
  5. b. Increasing.
  6. c. Increasing returns to scale.
  7. b. It will buy all labor and no capital.
  8. e. All of the above are correct.
  9. d. For the cost function CT(Q) = 8Q3 – 3Q2 + 10Q + 100, all of the above are correct.
  10. c. The long-run average cost curve has a U-shape because there are increasing returns to scale up to a certain level of production and decreasing returns beyond that level.
  11. b. If a firm wants to minimize costs and RMST < w/r, it should use more of factor K and less of L.
  12. b. If |RMST| = K + 8 and at the optimum K = 2, L = 10, and CT = 140, then w = 10 and r = 20.
  13. a. For the production function Q = 4L1/2 K1/2, there are increasing returns to scale.
  14. b. When the long-run average and marginal cost functions intersect, the average cost is at its minimum.
  15. b. For the production function Q = 6L + 2K, with factor prices w = 4, r = 2, and total cost 40, the optimal factor demands are L = 10, K = 0.

Additional Problems

  1. c. The company produces at the technical optimum.
  2. d. It should choose 1,500 units of labor and 7,500 units of capital.
  3. a. Straight lines with a negative slope.
  4. a. Decreasing returns to scale and diseconomies of scale.
  5. b. Increasing.
  6. c. Increasing returns to scale.
  7. b. It will buy all labor and no capital.
  8. e. All of the above are correct.
  9. d. For the cost function CT(Q) = 8Q3 – 3Q2 + 10Q + 100, all of the above are correct.
  10. c. The long-run average cost curve has a U-shape because there are increasing returns to scale up to a certain level of production and decreasing returns beyond that level.
  11. b. If a firm wants to minimize costs and RMST < w/r, it should use more of factor K and less of L.
  12. b. If |RMST| = K + 8 and at the optimum K = 2, L = 10, and CT = 140, then w = 10 and r = 20.
  13. a. For the production function Q = 4L1/2 K1/2, there are increasing returns to scale.
  14. b. When the long-run average and marginal cost functions intersect, the average cost is at its minimum.
  15. b. For the production function Q = 6L + 2K, with factor prices w = 4, r = 2, and total cost 40, the optimal factor demands are L = 10, K = 0.

More Practice Problems

  1. c. The company produces at the technical optimum.
  2. d. It should choose 1,500 units of labor and 7,500 units of capital.
  3. a. Straight lines with a negative slope.
  4. a. Decreasing returns to scale and diseconomies of scale.
  5. b. Increasing.
  6. c. Increasing returns to scale.
  7. b. It will buy all labor and no capital.
  8. e. All of the above are correct.
  9. d. For the cost function CT(Q) = 8Q3 – 3Q2 + 10Q + 100, all of the above are correct.
  10. c. The long-run average cost curve has a U-shape because there are increasing returns to scale up to a certain level of production and decreasing returns beyond that level.
  11. b. If a firm wants to minimize costs and RMST < w/r, it should use more of factor K and less of L.
  12. b. If |RMST| = K + 8 and at the optimum K = 2, L = 10, and CT = 140, then w = 10 and r = 20.
  13. a. For the production function Q = 4L1/2 K1/2, there are increasing returns to scale.
  14. b. When the long-run average and marginal cost functions intersect, the average cost is at its minimum.
  15. b. For the production function Q = 6L + 2K, with factor prices w = 4, r = 2, and total cost 40, the optimal factor demands are L = 10, K = 0.

Even More Problems

  1. c. The company produces at the technical optimum.
  2. d. It should choose 1,500 units of labor and 7,500 units of capital.
  3. a. Straight lines with a negative slope.
  4. a. Decreasing returns to scale and diseconomies of scale.
  5. b. Increasing.
  6. c. Increasing returns to scale.
  7. b. It will buy all labor and no capital.
  8. e. All of the above are correct.
  9. d. For the cost function CT(Q) = 8Q3 – 3Q2 + 10Q + 100, all of the above are correct.
  10. c. The long-run average cost curve has a U-shape because there are increasing returns to scale up to a certain level of production and decreasing returns beyond that level.
  11. b. If a firm wants to minimize costs and RMST < w/r, it should use more of factor K and less of L.
  12. b. If |RMST| = K + 8 and at the optimum K = 2, L = 10, and CT = 140, then w = 10 and r = 20.
  13. a. For the production function Q = 4L1/2 K1/2, there are increasing returns to scale.
  14. b. When the long-run average and marginal cost functions intersect, the average cost is at its minimum.
  15. b. For the production function Q = 6L + 2K, with factor prices w = 4, r = 2, and total cost 40, the optimal factor demands are L = 10, K = 0.