towards mastery in the practice of problem solving

Assessments

MODULE 4 Technology
1. You are the manager of 2 small stores with production functions q = K¼L¼ and a larger store with production function q = 2K¼L¼. You hire capital for $4, labour for $1. When you took over this role, your boss told you that Q = 24 was the profit maximizing output for this multi-plan firm: 24 = q1 + q2 + q3. Now, the price of labour rises to $4. Provide (i) Isoquant/Isocost diagrams, (ii) Total Cost and (iii) Marginal Cost diagrams. Illustrate the substitution effect (point a to b) and output effect (point b to c) on these diagrams. Explain why your firm uses less capital even when the price of labour increases. (September 2010) For the production function q = K2 + L2 (A) Demonstrate that the elasticity of substitution is negative. (B) Provide a labelled diagram showing the q = 100 isoquant (C) Briefly explain what a negative value means for σ 3. 4. A special production function is q = min( 80K, 4L1 + 2L2). Discuss the production process described by this function. Is this production function constant returns to scale? Five-year-old Jack has set up a hot chocolate stand outside his home. His customers like hot chocolate made in only one way, one unit of chocolate and 3 units of milk to go into each unit of hot chocolate. Jack’s mother, Naomi, provides him with heat, cups and cleaning free of charge. However, she charges him $0.25 for each unit of chocolate and $0.50 for each unit of milk. What are the returns to scale for his production function? (September 2008) Please answer both of the following questions. Provide clearly written, concise answers (maximum 100 words each). Provide diagrams as appropriate. (a) How are the ideas of diminishing marginal productivity and returns to scale related? Can a firm that has diminishing marginal products for all inputs still exhibit increasing