Please provide an explanation QUESTION 4: The utility curve is as follows The prices and income...

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QUESTION 4: The utility curve is as follows The prices and income are as follows 2 1-80 (a) Write down BC (b) Does this indifference curve exhibit DMRS? (c) What is the utility maximizing quantity of X and Y?

business economics

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Answer 1

Answer #1

a) Budget constraint is given by income = price of good 1 x quantity of good 1 + price of good 2 x quantity of good 2

80 = 2X + 4Y

simplified into

40 = X + 2Y

b) Here MRS = -MUX/MUY = -dU/dX divided by dU/dY

= -Y/X. Now DMRS implies diminshing MRS. MRS is decreasing for X when preferences are convex. Here utility function shows convex preferences because MRS is inversely related to X. This can be noted from the fact that as X rises MRS which is -Y/X falls. Hence the utility function shows DMRS

c) Optimal choice has |MRS| = PX/PY

Y/X = 2/4 or X = 2Y

Use this relation in the budget line

40 = 2Y + 2Y

This gives Y* = 40/4 = 10 units and X* = 2*10 = 20 units.

Optimal bundle is (20, 10).

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Answer 2

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