Question 1.6. The Ace Transformation Company can produce guns(y1), or butter (32), or both; using labor(a), as the sole input to the production process. Feasible production is represented by a production possibility set with a frontier x= vgi+32 (a) Write the production function on the implicit form G(y1, y2, 33)=0. Does G satisfy Assumptions 2.1 and 2.2? (b)Suppose that the company faces the following union demands. In the next year it must purchase exactly i units of labor at a wage rate w; or no labor will be supplied in the next year. If the company knows that it can sell unlimited quantities of guns and butter at prices p1 and p2 respectively, and chooses to maximize next year's profits, what is its optimal production plan? Question 1.7. A consumer has a utility function u(a1, 2)=-+- (a) Compute the ordinary demand functions (b) Show that the indirect utility function is -(VPi+VP2)2/I (c)Compute the expenditure function (d) Compute the compensated demand functions Question 1.8. A consumer has expenditure function e(p1, P2, u)=Pip2u. What is the value of b? Question 1.9. Suppose the consumer's utility function is homogeneous of degree 1 Show that the consumer's demand functions have constant income elasticity equals 1 Question 1.10. What axiom is violated by (0,0.75;100,0.25)>[0,0.5;(0,0.5;100,0.5),0.5Question 1.6. The Ace Transformation Company can produce guns ( y1 ), or butter ( y2 ), or both; using labor ( x ), as the sole input to the production process. Feasible production is represented by a production possibility set with a frontier x = sy2 1 + y2 2. (a) Write the production function on the implicit form G(y1, y2, y3)=0. Does G satisfy Assumptions 2.1 and 2.2? (b) Suppose that the company faces the following union demands. In the next year it must purchase exactly x¯ units of labor at a wage rate w; or no labor will be supplied in the next year. If the company knows that it can sell unlimited quantities of guns and butter at prices p1 and p2 respectively, and chooses to maximize next year’s profits, what is its optimal production plan? Question 1.7. A consumer has a utility function u(x1, x2) = − 1 x1 − 1 x2 . (a) Compute the ordinary demand functions. (b) Show that the indirect utility function is −( √p1 + √p2)2/I. (c) Compute the expenditure function. (d) Compute the compensated demand functions. Question 1.8. A consumer has expenditure function e(p1, p2, u) = p 1/4 1 pb 2u. What is the value of b ? Question 1.9. Suppose the consumer’s utility function is homogeneous of degree 1. Show that the consumer’s demand functions have constant income elasticity equals 1. Question 1.10. What axiom is violated by (0, 0.75; 100, 0.25) " [0, 0.5; (0, 0.5; 100, 0.5), 0.5] ? 2