mt-Sample-on-website_KEY

# mt-Sample-on-website_KEY - ECON 331 Sample Midterm Exam...

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ECON 331 Sample Midterm Exam Spring 1998 Selected Answers and Hints: 1. Given the matrix A = 2 6 6 6 6 6 4 1 0 4 3 3 0 1 0 6 9 0 0 1 1 2 0 0 2 1 1 0 0 0 1 0 3 7 7 7 7 7 5 The determinant: j A j = 3 2. Consider the following two market model Q d 1 = 20 P 1 + 2 P 2 Q s 1 = 2 P 1 2 Q d 2 = 18 2 P 2 + 3 P 1 Q s 2 = 2 + 4 P 2 (a) HINT: Look at the signs of the cross partials @Q i j (b) Use Cramer&s rule to ±nd the inverse demand func- tions P 1 = P 1 ( Q 1 ;Q 2 ) P 2 = P 2 ( Q 1 ;Q 2 ) : Solution " P 1 P 2 # = " 1 2 Q 1 + 1 2 Q 2 19 3 4 Q 1 + 1 4 Q 2 39 2 # 3. Consider the following: (a) Let q = f ( L ) be the short run production function where L represents labour, the only input. use cal- culus to show that when MP L > AP L , AP L is rising and MP L < AP L , AP L is falling. HINT: See Chapter 7 (b) When MP L = AP L , AP L is assumed to be at a maximum and not a minimum. What assumption about the second derivative of f ( L ) ensures this result? What is the economic expression for this result? HINT: Look at a graph of
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