A firm produces quantity Q of breakfast cereal using labour L and material M with the production function $Q = (ML)^2 + M + L$. (a) Find the marginal product functions for this production function. (6 marks) (b) What is the marginal rate of technical substitution of L for K for this production function? (5 marks) (c) What type of returns to scale arises from this production function? (6 marks) PART B Compare and contrast the short-run supply curve and the long run supply curve of the firm. Use appropriate diagrams to explain your answer. (8 marks) Total: [25 marks]
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To find the marginal product functions, we need to take the partial derivatives of the production function with respect to each input variable. Taking the partial derivative with respect to labor L: ∂Q/∂L = M + 1 Taking the partial derivative with respect to Show more…
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Statement of Question 1 One of the key concepts in production theory is the production function Q = f(L, K) and the corresponding isoquants. The Marginal Rate of Technical Substitution (MRTS) is the ability of the firm to replace capital for labour while maintaining the same output level. Figure 1 shows the isoquant for Q = 100. There are two tangent lines: one at point A = (3, 6) and another at point B = (5, 4). On the isoquant for Q = 100, the slope falls when we move from the input combination A = (3, 6) to B = (5, 4). Perform the following tasks: (a) Calculate the value of the MRTS at points A and B. [10 marks] (b) What is incorrect in the Statement of Question 1? [10 marks]
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