Use the willingness-to-pay information about the buyers (Ariel, Bridget, and Connie) and the willingness-to-accept information about the sellers (Daniel, Etienne, and Franklin) below to construct a "stepped" demand and supply diagram like this one from my notes on Unit #7. (You'll also have one question to answer below.) Willingness-To-Pay information Ariel Bridget Connie willingness-to-pay $5 $7 $9 for the 1 widget willingness-to-pay $4 $6 $7 for the 2" widget willingness-to-pay $3 $4 $5 for the 3 widget willingness-to-pay $2 $3 $4 for the 4 widget willingness-to-pay $1 $2 $3 for the 5" widget Willingness-To-Accept information A Daniel Etienne Franklin willingness-to-4. Vacancy costs and the labor market. Consider the search-theoretic model of the labor market of Diamond {1982), Mortensen (1982} and Pissarides (1985). a. The equilibrium tightness of the labor market, 6", solves the following equation -ny-w luWWW Plot the left and the right hand side of the above equation as functions of 9 and identify 6'. k=so b. Using the same yaph as before, identify the effect of an incraese in the vacancy cost it: on the equilibrium tightness of the labor market. Interpret your nding. c. The equilibrium unemployment, n", and the equilibrium vacancies, v", solve simultaneously the following system of equations Plot the solutions to these two equations in a graph that has it on the horizontal axis and v on the vertical axis (Le. plot the Beveridge curve and the market tightness curve]. Identify n\" and 11*. (1. Using the same graph as before, illustrate the eifect of an increase in the vacancy cost I: on the equilibrium unemployment and vacancies. Interpret your ndings. e. Should the government intervene to lower unemployment in response to an increase in k? 4. (30 points) Consider the following game. There are ten dollars to divide. Two players are each required to simultaneously name an integer between 0 and 10. The player who names the higher number gets to keep the money. If they name the same number, the money is equally shared between them. (a) Describe the set of players N, the set of strategies { Silien, and the payoff function QuitiEN. (b) Are there strategies that are strictly dominated? Demonstrate your reasoning. What are the resulting strategies after iterated elimination of strictly dominated strategies? (c) Find the best responses (correspondence) for each player. That is, find the strategies that maximize a player's payoff given what the other player does. (d) Find the Nash equilibria of the game. (e) Suppose now the game is changed. Whenever there is a tie, each player receives nothing. Answer the same questions in parts (b) and (c). Find the pure-strategy Nash equilibria of the game.30 -12 cm 10. Simplify Calculate, correct to one decimal place: (a) the length of CD; 11. Simplify (b) the length of AB; (c) the area of triangle BCD; (3 max 12. Write si (d) the size of Z BDC. (2 max leaving 12015 PPT Now 25. SURDS 13. Simpli 1. Simplify (1+3)(1-13) Hence evaluate 1+ 1/3 to 3 s.f. given that v3 = 1.7321 (1 mark 14. Simp 2. If V14 V14 [196 PPZ Nia. V7 -12 17+12 = av7 +bv2 , find the values of a and b where a and b are and c rational numbers. (4 marks 15. Simp 3. Simplify as far as possible, leaving your answer in the form of a surd [1997 PP2 Na. 13 14 - 2V/3 V14+2V3 16. Simp 2 marks [1998 PP2 Na.] 4. Given that a = V3 and b = V13 , express 2V/3 -6739 in terms of a and b and simplify the answer. 3 marks 1. Wit 12003 PP2 No. 14 5. Without using mathematical tables, simplify_ 2 2 in the form avb (3 marks) 3 - 17 3+17 12004 Pp? No. 1of 2. So 6. Without using Mathematical tables, simplify V63 + 172 (3 marks) V32 + 128 3. Fi 7. Without using a calculator or mathematical tables, simplify 3V2 - 3 2V/3 - V2