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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

3. A firms production function is given by y-z, 1z14. Input prices are w, and w2. Input 2 is fixed at 256. 1/4 a) Derive the firms variable cost function. b) If w1 8 and w2 5, what is the least cost of producing 40 units of output? c) At these prices and output, what is the marginal cost?

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