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Agent's preferences are represented by the following utility function: U(x, y) = x?y?

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Agent's preferences are represented by the following utility function: U(x, y) = x?y?. The prices of = goods x and y are respectively Px = 40 and py = 100. = = a) Suppose that agent's weekly income is m = 200 and draw the budget line. What is the slope of the budget line? Suppose now that agent's weekly income is m' = 400 and draw the new budget line. Comment on how the new budget line has changed with respect to the original budget line. b) Compute the Marginal Rate of Substitution and given that agent's monthly income is m = 1600 find the optimal consumption bundle. 1 [Hint: U$ = v/, Tilbudt ==1/ and Uy X2 = 2y? : % 1 1 ] 2x2 c) Suppose that price of good x increases. Show graphically the change in the optimal consumption bundle and indicate the substitution effect and the income effect.