ps7_fall11 - Department of Economics Columbia University...

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Unformatted text preview: Department of Economics Columbia University W3211 Fall 2011 P r ob l e m Se t 7 I n t e r m e d i a t e M i c r o e co n o m i cs P r of . Se y h a n E A r k on a c 1. Suppose that the minimum wage covers all sectors of the economy; however, for unionized laborers, the minimum wage is ineffective. That is, the union wage is already above the minimum wage. Analyze the impact of an increase in the minimum wage on both the unionized and non-unionized labor markets. (Assume that the higher minimum wage is still ineffective in the unionized sector and that union and nonunion labor are substitutable.) 2. Suppose there are only two goods – Food ( F ) and Shelter (S). The demand equations for these two goods depend on their prices, p F and pS as follows: D F (p F , pS) = 10 – 2p F – pS D S (p F , pS) = 10 – p F – 2pS The supply curves depend only on their own prices: S F (p F ) = p F SS (pS) = 5pS Determine the equilibrium price and quantity of these goods. 3. Consider trade between two consumers (1 and 2) and two goods, X and Y. Suppose the total quantities of each good are 100 units. Each consumer has Cobb-Douglas preferences given by: U (X,Y) = XY What is the shape of the contract curve, i.e. derive the equation? How does the contract curve change if consumer one has the utility function 2 U (X,Y) = X Y while the other consumer’s preferences are as before? Again, derive the equation for the contract curve. 4. Consider a two-trader/two-good exchange economy in equilibrium. If the endowment point moves to the north east, i.e. the endowment quantities to one of the consumers increase, can we determine the direction in which the equilibrium quantities will change? Demonstrate your answer with a graph including the relevant indifference curves, contract curve and price line. 5. Sarah and Andrew are two traders in a pure exchange economic with two goods, Bikes (B) and Computers ( C ). Sarah's preferences are described by the Cobb-Douglas Utility function: 1/3 2/3 U S = BS C S Andrew's preferences are given by: 1/2 U A = B A½ C A Assume the price of Bikes is 1 and the price of computers is p. The initial endowments are B A = 10, BS = 20, C A = 20 and C S = 10. Solve for the competitive equilibrium prices (relative prices) and quantities. 6. Consider a society consisting of just a farmer and a tailor. The farmer has 10 units of food but no clothing. The tailor has 20 units of clothing but no food. Suppose each has the utility function U = F * C. The price of clothing is always $1. If the price of food is $3, does a competitive equilibrium exist? If not, what will happen to the price of food? 7. Two individuals, Fred and Helen, in an economy with no production, each have the utility function U 10XY. Prices of both X and Y are set at $1. Initial endowments for Fred are 10 units of X and 6 units of Y. Helen has 8 units of X and 12 units of Y. Show that this initial endowment is not on the contract curve. 8. Suppose Jenna and Karen both regard peanut butter and jelly as perfect complements at a 1:1 ratio. Show using an Edgeworth box diagram that if Jenna receives 10 peanut butter and no jelly, and Karen receives 10 jelly and no peanut butter, after trading, they will each end up with 5 units of each. 9. Suppose that David and Harry consume oranges and apples. David views the two as perfect complements. Harry views them as perfect substitutes. Each reaches his hand into a bag and selects six pieces of fruit but cannot see what they have chosen until it is in their basket. Assume that the bag the bag only has 12 pieces of fruit – 6 apples and 6 oranges. If they apply the Pareto criterion to wealth distribution, what will be their final endowment after trading? 10. In Problem 9, if Harry decides not to follow the Pareto criterion and each must pay a very small fee for each trade, what will be the effect on trading? F ol l ow i ng q u est i ons w i l l not b e g r a d e d , t h e y a r e f o r you to p r a c t i c e a n d w i l l b e d i sc usse d a t t h e r e c i t a t ion : 1. 2. 3. 4. 5. 6. Ch. 10 Ch. 10 Ch. 10 Ch. 10 Ch. 10 Ch. 10 question 10 question 11 question 13 question 19 Question 23 Question 26 ...
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This note was uploaded on 01/16/2012 for the course ECON W3211 taught by Professor Elmes during the Fall '09 term at Columbia.

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