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Suppose that there are two goods, X and Y. The utility function is U = XY...

Suppose that there are two goods, X and Y. The utility function is U = XY + 2Y. The price of one unit of X is P, and the price of one unit of Y is £5. Income is £60. Derive the demand for X as a function of P.

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Answer #1

U = XY + 2Y

Budget line: 60 = PX + 5Y

Utility is maximized when MUX / MUY = Px / Py = P / 5

MUX = U/X = Y

MUY = U/Y = X + 1

MUX / MUY = Y / (X + 1) = P / 5

PX + P = 5Y

Subtituting in budget line,

60 = PX + PX + P

60 = 2PX + P

2PX = 60 - P

X = (60 - P) / 2P [Demand function for X]

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