please look the numbers correctly and show all your work and steps on how you go
ID: 1107209 • Letter: P
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please look the numbers correctly and show all your work and steps on how you got to the answer.
2. Consider Bridget, who has preferences that can be described by the utility function Uny) x 4y.6 and, therefore, has the Marshallian demand functions x.. e and y-AM . 'ya, and, Py Bridget also has an expenditure that can be described by E(Px, Py, U)-1.96up, *p. Initially Bridger is facing prices such that Px-1, Py 2, and her income is 30. Then, the price of y increases to $3, all else equal. Find the substitution and income effects associated with this increase in price. To do this you will need to derive Bridget's compensated demand functions. A. B. What level of income will compensate Bridget for the change in the price of x?Explanation / Answer
For a utility function U = x^0.4y^0.6, and budget line xPx + yPy = M, we have a demand function for x which is x* = 0.4M/Px and for y* = 0.6M/Py
Original income M = 30 Py = 2 and Px = 1.
x* =0.4*30/1 = 12 units and y* = 0.6*30/2 = 9 units
New price = Py* = 3. New demand x** = 0.6*30/3 = 6 units
Total price effect = -3 units
Substitution effect
ys = demand for y (at new price and new income) – demand for y (at old price and old income)
New income = The change made in old income to make old bundle purchasable at new price.
Change in income = old demand for x* x (price change) = 9*(1) = 9. Hence new income is $39.
Substitution effect
xs = demand for y (at new price and new income) – demand for y (at old price and old income)
= 0.6*39/3 - 0.6*30/2
= -1.2 units
Income effect
xm = demand for x (at new price and old income) – demand for x (at new price and new income)
= 0.6*30/3 - 0.6*39/3 = -1.8 units
Hence total effect is -3 units.
Compensating variation is the amount of money necessary to be given to the consumer to keep her original bundle. The original bundle was 9 units of x so at the new price of $3 per unit, this bundle would have required $27 more than the current income. So the compensating variation is $27.
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