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  3. charlotte spends her income of 2400 on clothing good x...

Question: charlotte spends her income of 2400 on clothing good x...

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Charlotte spends her income of $2400 on clothing (good x), and the composite good (good y ). The utility Charlotte receives from consuming a basket of clothing and the composite good is, U(x, y ) = 2√ x + y 300. The corresponding marginal utilities are, MUx = 1 √ x and MUy = 1 300.

REQUIRED: (a) Is the ‘principal of diminishing marginal utility’ satisfied for both clothing and the composite good? Briefly explain. (2 mark)

(b) Derive an expression for Charlotte’s marginal rate of substitution. Is the marginal rate of substitution diminishing? Briefly explain. (2 marks)

(c) Find Charlotte’s optimal consumption basket when the price of clothing is Px1 = $50, and the price of the composite good is Py = $1. (3 marks)

(d) Find Charlotte’s optimal consumption basket when the price of clothing increases to Px2 = $60 (the price of the composite good remains Py = $1). (3 marks)

(e) Find the income and substitution effects for the price increase. Is clothing a normal good? Briefly explain. (5 marks)

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