As you will see result is given for question 1. Your task is to mathematically s

Question

As you will see result is given for question 1. Your task is to mathematically show how to get to that result Question 1 Please show mathematically that Madison's demand functions for good B and good Z will be: B = 0.8 PB 2- 0.2_ .. given that she has the following utility function and budget constraint where Y=income, pB-price of good B and pz-price of good z. Question 2 Use the above demand functions to derive the quantity demanded of good B under the following circumstances (a) The price of good B is $5 and the income is $100 (b) The price of good B is $10 and the income is $100 (c) The price of good B is $5 and the income is $200 Your answers to (a)-(c) may be helpful when answering the following (d) Does the demand function for good B comply with the Law of demand? Why/why not? (e) Is good B a normal or inferior good? Why?

Explanation / Answer

Demand function for good B = 0.8Y / PB

(a) B = (0.8 x 100) / 5 = 16

(b) B = (0.8 x 100) / 10 = 8

(c) B = (0.8 x 200) / 5 = 32

(d) Using the results in (a) and (b), Income remaining unchanged, when price of good B increases, quantity demanded of good B decreases. So good B follows the law of demand.

(e) Using the results in (a) and (c), price of good B remaining unchanged, when income increases, demand for good B increases. So good B is a normal good.

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