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Question: tutorial2 chapter 7 part 1 key concepts and equations production...

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TUTORIAL2 Chapter 7 Part 1 Key Concepts and Equations: Production Isoquant: shows all combinations of input quantities that yield the same level of output. Higher isoquant: higher level of output Marginal Rate of Technical Substitution: MRTS is the slope of the isoquant at any input combination. It tells us the rate at which we must increase the qty of input 2 per unit decrease in qty of input 1. MRTS diminishes as we move down the isoquant from left to right MRTS = MP(Z1)/ MP(zz) A linear isoquant means MRTS is constant- a linear isoquant inputs are perfect substitutes. An L-shaped isoquant means MRTS cannot be defined at the kink -inputs are perfect compliments 3 types of returns to scale: increasing- on downward sloping portion of the LRAC constant on the flat portion of the LRAC and decreasing- on the upward sloping portion of the LRAC Conditional input demand functions: the demand for each input as a function of y, W1 and w2. There are no zs in these equations The slope of the isocost is w/W2 Two principles of cost minimization The cost minimizing input bundle is on the isoquant y F(z1 72). The MRTS is equal to w/w2 at the cost minimizing bundle slope of the isoquant slope of the isocost line MP(z1) / MP(Z2) - W,/W2 If the price of one input changes, the optimal combination of inputs will change. Total cost will change If goods are perfect substitutes, the optimal input mix will be a corner solution. When isoquants are convex, we get an interior solution

1 a) A fim has the production function y ZiZ and faces input prices w1 and w2 Derive the conditional input demand functions for both inputs. 1/2

b) If w, S5 and w2-$10, what is the minimum cost of producing 27 units of output?

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