1.Clara\'s utility function is U(X,Y) = (X + 2)(Y +1). a) Write an equation for
ID: 1190702 • Letter: 1
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1.Clara's utility function is U(X,Y) = (X + 2)(Y +1). a) Write an equation for Clara's indifference curve that goes through the point (X,Y) = (2, 8). b) Suppose that the price of each good is one and that Clara has an income of 11. Write an equation that describes her budget constraint. c) Find an equation the describes Clara's MRS for any given commodity bundle (X,Y). d) Use the equations in parts b) and c) to solve for Clara's optimal bundle. 1.Clara's utility function is U(X,Y) = (X + 2)(Y +1). a) Write an equation for Clara's indifference curve that goes through the point (X,Y) = (2, 8). b) Suppose that the price of each good is one and that Clara has an income of 11. Write an equation that describes her budget constraint. c) Find an equation the describes Clara's MRS for any given commodity bundle (X,Y). d) Use the equations in parts b) and c) to solve for Clara's optimal bundle. 1.Clara's utility function is U(X,Y) = (X + 2)(Y +1). a) Write an equation for Clara's indifference curve that goes through the point (X,Y) = (2, 8). b) Suppose that the price of each good is one and that Clara has an income of 11. Write an equation that describes her budget constraint. c) Find an equation the describes Clara's MRS for any given commodity bundle (X,Y). d) Use the equations in parts b) and c) to solve for Clara's optimal bundle.Explanation / Answer
a) at (2,8) Clara's utility will be (2+2)(8+1) = 36 so now 36 = (X+2)(Y+1) ; Y = 36/(X+2) - 1 this is the equation for Clara's indifference curve that goes through the point (X,Y) = (2, 8).
b) PxX + PyY = I; 1*X + 1*Y = 11; X + Y = 11 this the equation for budget constraint
c) MRS =MUx/MUy now MUx = dU/dX = d(XY + X + 2Y + 2)/dX = Y + 1; now MUy = dU/dY = d(XY + X + 2Y + 2)/dY = X + 2 so MRS = (Y+1)/(X+2)
d) For optimal bundle MRS = Px/Py = 1 sp Y+1 = X + 2 now solving eq found in b) and c) we get Y= 6 and X=5
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