Suppose there are two consumers, A and B. There are two goods, Good X and Good...

 

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Suppose there are two consumers, A and B. There are two goods, Good X and Good Y. X is the quantity of Good X, and Y is the quantity of Good Y. Suppose the consumers' utility functions are given by: UA(X,Y) =X+4Y UB(X,Y) = 2X + Y Explain under what two conditions is it possible for an allocation to be Pareto Efficient. Be specific. 3. (16 points) A firm has the production function q = L1/2K1/2. The firm can purchase labor, L at a price w = 9, and capital, K at a price of r=4. a) (4 points) What is the firm's total cost function? b) (12 points) Sketch the graph of the firm's isoquant for q = 6 units of output, and on the same graph sketch the firm's isocost line associated with the total cost of producing q = 6 units of output. To get this total cost, you must use the Total Cost function from part a). Also, identify L* and K* on your graph. Make sure your graph is neatly and accurately drawn and carefully labeled. Suppose there are two consumers, A and B. There are two goods, Good X and Good Y. X is the quantity of Good X, and Y is the quantity of Good Y. Suppose the consumers' utility functions are given by: UA(X,Y) =X+4Y UB(X,Y) = 2X + Y Explain under what two conditions is it possible for an allocation to be Pareto Efficient. Be specific. 3. (16 points) A firm has the production function q = L1/2K1/2. The firm can purchase labor, L at a price w = 9, and capital, K at a price of r=4. a) (4 points) What is the firm's total cost function? b) (12 points) Sketch the graph of the firm's isoquant for q = 6 units of output, and on the same graph sketch the firm's isocost line associated with the total cost of producing q = 6 units of output. To get this total cost, you must use the Total Cost function from part a). Also, identify L* and K* on your graph. Make sure your graph is neatly and accurately drawn and carefully labeled.