...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...
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