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Suppose the production possibility frontier for guns (x) and butter (y) is given byx2+ 2y2= 900.a. Graph this frontierb. If individuals always prefer consumption bundles in which y = 2x, how much x and y will be produced?c. At the point described in part (b), what will be the RPT and hence what price ratio will cause production to take place at that point? (This slope should be approximated by considering small changes in x and y around the optimal point.)d. Show your solution on the figure from part (a).
Answer :- a) Their frontier will be a circle as shown :- b) We have :x2+ 2y2= 900 (1) Also,y = 2x (2) substituting (2) in (1) x2 + 8×2 = 900…

9×2 = 900 x2 = 100 x = 10 Substituting x = 10 in (2) We get, y = 20 Hence, x = 10 and y = 20.

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