The Hormsbury Corporation produces calculators at its factory. Wages are $12 per hour and calculator making equipment (a computer-controlled machine) rents for $4 per hour. The production function is
where q = boxes of calculators per week, K = hours of calculator equipment used, and L = hours of labour.
1. Determine the cost-minimizing capital-labour ratio.
2. Graph the company's isoquant for q = 1000 and the isocost line tangent to this isoquant. What is the minimum cost of producing 1000 boxes of calculators?
3. Show the firm's expansion path.
4. Suppose that capital is fixed at the level that minimizes the cost of producing 1000 boxes of calculators. Explain what the firms would do in the short run in order to produce 1500 boxes of calculators per week. Give the new input mix and cost of production.
5. Draw the long-run and short-run average cost curves for this firm.