Midterm1ans

# P y 6 and x 8 total spending on good x 28 16 total

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P Y =6 and X = 8. Total spending on good X = 2*8 = 16 Total spending on good Y = 6*6 = 36 Suppose now that the price of good X becomes \$4 while the price of good Y does not change. c) Identify (on a diagram) the substitution effect and income effect associated with the increase in the price of good X. (8 marks) See class note or assignment 1 answer key. It is up to the student to draw the effects for a normal or an inferior good. Key point is if the good is inferior good, then the 2 effects must

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be in opposite direction. If it is normal good then the 2 effects must be in the same direction. Suppose now that we are able to derive Tom’s demand for good X as: Px = 26 – 3X T (where X T is Tom’s demand for good X). Also, Peter (Tom’s brother) has identical utility function and budget like Tom. d) Prove that the market (consisting of 2 consumers: Tom and Peter) aggregate demand function takes the following form: 3 26 2 X AGG P X . (6 marks) Since Peter has identical utility and budget, he must have identical demand function for good X. Thus the aggregate market demand for good X is: 52 2 2 3 3 AGG T P T X X X X X P Or 3 26 2 X AGG P X e) What is the supply curve so that the market equilibrium quantity and price are 16 and 2 respectively? (4 marks) An upward sloping supply curve normally takes the following form: P X = a + bX (linear). Since it starts at the origin, a = 0. The supply curve is thus just Px = bX. With X = 16 and Px = 2, b = 1/8. Or the supply curve is Px = 1/8X. Question 2 (30 marks) Suppose the ORANGE COMP INC. has the following production function: 1/2 1/2 ( , ) 4 Q K L K L . It also takes market wage (w) and rent (r)as given where w=2 and r = 4.
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• Fall '12
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