Pauline is considering becoming a member of a CD club, which offers discounts on CDs. There is a membership fee of 100 but then each CD is only 10.

Transcription

1 Problem 1 (20 points) Pauline loves music. Her income is 300. Let x1 denote the quantity of CDs she buys and x2 the quantity of other goods. She has a positive marginal utility for CDs and other goods and her marginal rate of substitution is decreasing as x increases. The price of a CD is 20. At this price she consumes 10 CDs and spends 100 on the other goods. Pauline is considering becoming a member of a CD club, which offers discounts on CDs. There is a membership fee of 100 but then each CD is only 10. Use consumer theory to find out how becoming a member of the club will change Pauline s consumption pattern and determine whether or not she should join the club

2 Problem 2 (20 points = ) A consumer buys two goods: food and clothing. His utility function is U(x,y) = xy, where x is the quantity of food and y is the quantity of clothing he consumes. The price of food is px and the price of clothing is py. The consumer s income is I. a. What is his marginal utility for food? What is his marginal utility for clothing? b. What is the demand function of the consumer for food? What is the demand function of the consumer for clothing? Draw a graph of the demand functions when I=120 and I=200. c. Is food a normal or an inferior good and why? - 2 -

3 Problem 3 (30 points = ) George loves veal cutlets and fries. The price of veal cutlets is pv=1, while the price of fries is pf=5. George has an income m of 200. His demand functions for veal cutlets and fries are respectively equal to: x x v G f G 2m ; 5pv 3m. 5p f a. The price of veal cutlets increases to Determine the optimal bundle at the original prices (pv=1 and pf=5). 2. Determine the optimal bundle at the new prices (pv=2 and pf=5). 3. Calculate the substitution effect for veal cutlets. 4. Calculate the income effect for veal cutlets

4 b. Suppose that, instead of an income, George has an endowment of 100 veal cutlets and 20 fries. Calculate the endowment income effect for veal cutlets associated with the price increase from 1 to 2 for veal cutlets. Consider an exchange economy, where in addition to George as described above, there is also Tom (but no one else). George has an endowment of 100 veal cutlets and 20 fries. Tom has an endowment of 50 veal cutlets and 58 fries. Tom s utility function is UT(x v T, x f T)= min{2 x v T, x f T}. c. Rewrite the Tom s utility function in terms of the consumption bundle of George, i.e., in terms of x v G and x f G

5 d. Give an equation for the set of Pareto optimal bundles and draw the contract curve in an Edgeworth box. Put veal cutlets on the horizontal axis and fries on the vertical axis. Measure goods for George from the lower left corner of the box and goods for Tom from the upper right corner of the box. Also represent the initial endowment allocation on the Edgeworth box. e. Suppose the price of veal cutlets is set equal to 1 (numeraire price). 1. Determine the demand functions of George as a function of pf (independently of m). 2. Determine quantities consumed by George and Tom at the competitive (Walrasian) equilibrium. Represent this final allocation on the Edgeworth box

6 Problem 4 (30 points = ) The demand for tricycles for little kids depends on the price according to the following equation D(p) = p (assume that a fractional quantity can be consumed). a. Assume (only for this sub-question) that the market for tricycles is a pure competition market with constant marginal costs for the suppliers of 20 each. What is the deadweight loss when a tax for 10 per unit is introduced? The company A sells tricycles for little kids. The cost of production is described by the cost function C(y) = 100+y 2. b. Determine the supply function of company A when company A is a price taker. c. Suppose that company A is the only supplier of tricycles for little kids. Calculate the price it will charge and the quantity

7 d. Company B has the same cost function as company A and decides to also sell tricycles for little kids. Company A gets to determine its quantity first. Calculate company B s reaction function. Let ya be the output of company A and yb be the output of company B. e. Calculate the output of both firms when company A determines its quantity first. f. Calculate the output of both firms when they simultaneously determine their output levels