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MECON PS1 sol - Microeconomics 100A Problem Set 1 Solutions...

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Microeconomics 100A Problem Set 1 Solutions Due January 20, 2010 Professor Michael Noel University of California San Diego 1. Imagine the demand function for oranges for consumer i is given by Q i d = 100 – 10p 0 + 2p G + 4p A . + Y i . The current price of oranges, p 0 , is 1. The current price of a bag of grapes p G is 1, the current price of an apple p A is 1. Income is currently 20. a. How much is quantity demanded for consumer i at current prices? 116 = d i Q . b. Calculate the (2D) inverse demand curve for oranges, i.e. p 0 as a function of Q i d , holding all other prices and income equal to their current values. Draw this in a 2-D diagram with Q on the horizontal axis and p 0 on the vertical. What is the slope of the inverse demand curve? The inverse demand curve is given by 2 4 . 0 2 . 0 10 10 0 + + + - = d i Q p , which has slope - 0.1. c. Write down the (2D) demand curve Q as a function only of p G , holding all other prices and income equal to their current values. Draw this as an inverse demand curve with Q on the horizontal and p G on the vertical, holding other prices and income fixed at current values. What is the slope of this inverse demand curve? The demand curve is given by Q i d = 100 – 10 + 2p G + 4 + 20 . The inverse demand curve is given by 10 2 5 2 50 - - + + - = d i G Q p , which has slope 0.5.
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d. Write down the (2D) demand curve Q as a function only of p A , holding other prices and income fixed at current values. . Draw this inverse demand curve with Q on the horizontal and p A on the vertical. What is the slope of this inverse demand curve? The demand curve is given by Q i d = 100 – 10 + 2 + 4p A + 20 . The inverse demand curve is given by 5 5 . 0 5 . 2 4 25 - - + + - = d i A Q p , which has slope 0.25. e. Write down the (2D) demand curve Q as a function only of Y, holding all prices and fixed at current values. . Economists like to call this an “Engel curve”. Draw this Engle curve with Q on the horizontal and Y on the vertical. What is the slope of this inverse Engel curve?
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The Engel curve is given by Q i d = 100 – 10 + 2 + 4 + Y i . The slope of the inverse Engel curve is 1. f. Imagine consumer i gets a raise and her income rises to 30. Write down the new (true) demand function for oranges, i.e. Q as a function of all prices and income. Now that income has increased, has this (true, 5D) demand function shifted to the left or to the right?
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