Microeconomics q3

Question 3 Consider a production economy with two agents, Bunter and Quelch, and a factory. Each agent is endowed with one unit of labor, and the factory uses labor to produce Brawndo (good 1) and Soma (good 2) according to some production function. Both Bunter and Quelch only derive utility from the consumption of Brawndo and Soma, but not from labor, and each of them is entitled to half of the factory's prots. Denote by (551,932) the bundle of Brawndo and Soma, respectively, consumed by Bunter. Similarly, denote by (yhyg) the amount of Brawndo and Soma consumed by Quelch. Let Bunter's utility function be u(:vl, (5'2) 2 i i and let Quelch's utility function 921 1:2' 1 1 be "(Z/1W2) = ; E' Page 2 1. Suppose the factory can produce 3% units of good 1 when 21 units of labor are used as input, and 2% units of good 2 when 22 units of labor are used as input. Compute the Walrasian equilibrium of this economy and the utility of Bunter and Quelch. 2. Suppose now that the factory has become more efcient and can produce 21 units of good 1 when 21 units of labor are used as input, and up to 22 units of good 2 when 22 units of labor are used as input. Bunter and Quelch are concerned that this will make them worse off as less labor is required to make a certain level of output than before. Compute the new Walrasian equilibrium of this economy and the utility of Bunter and Quelch, and compare it with the answer obtained from (a). What is the new prot of the factory, and how does it compare with (a)