Assignment Task: Consumer Behaviour
Joe can allocate his time between working (H - hours worked) and leisure (L - hours spent in leisure), and spends all 24 hours per day doing one or the other. He earns a wage of w dollars per hour, which he spends entirely on consumption of all other goods (not including leisure time); he has no other source of income. Since we assume all goods are measured in dollar amounts, consuming Y dollars' worth of goods is at a price of $1 - it costs $1 to buy $1 worth of all goods.
His utility function is U= 3LY where Y is his total income. His MUL = 3Y and his MUY = 3L.
1) What levels of H and L does he choose in optimal? [Hint: optimality has to ensure 3 conditions here: budget constraint, time constraint and the tangency condition].
2) Now suppose Joe's industry goes into a rough phase and his boss has to slash Joe's wages to µ. Draw a diagram with leisure on the horizontal axis and all other goods on the vertical axis and the usual downward sloping indifference curve. Show i) the budget lines and the optimal choices for the two cases of before and after the wage cut ii) the substitution effect and income effect following the wage cut. [Hint: the expression from part b should tell you where the optimal point will be on the new budget line].
3) Briefly explain the substitution effect and income effect situation from part b with special reference to the income elasticity of leisure demand and the price elasticity of leisure demand.
4) Draw Joe's labor supply curve using the information from parts a and c.
Tutorial Questions:
1. Each week Troy selects the quantity of two goods X and Y that he will consume in order to maximize his utility. He spends his entire weekly income on these two goods.
Suppose you are given the following information about the choices that Troy makes over a three-week period:
|
|
X
|
Y
|
Px
|
Py
|
I
|
|
Week 1
|
10
|
?
|
3
|
1
|
50
|
|
Week 2
|
?
|
16
|
2
|
1
|
50
|
|
Week 3
|
9
|
12
|
2
|
1
|
30
|
How much Y in week 1 and how much X in week 2 should Troy be consuming? Why? Did Troy's Utility increase or decrease between weeks 1 and 2 and between weeks 1 and 3? Explain using a graph. Identify the income and substitution effects that result from a change in the price of good X (Hint: which weeks should you be using?) Draw the demand curve(s) for X using the above data. Draw the PCC and the ICC.
2. Each week Thomas selects the quantity of two goods X and Y that he will consume in order to maximize his utility. He spends his entire weekly income on these two goods.
Suppose you are given the following information about the choices that Thomas makes over a three-week period:
|
|
X
|
Y
|
Px
|
Py
|
I
|
|
Week 1
|
10
|
20
|
2
|
1
|
40
|
|
Week 2
|
7
|
?
|
2
|
2
|
40
|
|
Week 3
|
?
|
10
|
2
|
2
|
60
|
How much Y in week 2 and how much X in week 1 should Thomas be consuming? Why? Did Thomas's Utility increase or decrease between weeks 1 and 2 and between weeks 1 and 3? Explain using a graph. Identify the income and substitution effects that result from a change in the price of good X (Hint: which weeks should you be using?) Draw the demand curve(s) for X using the above data. Draw the PCC and the ICC.
3. Consider the U-functions below:
i) U(X, Y) = 4X2Y3 with MUx = 8XY3 and MUy = 12X2Y2.
ii) U(X, Y) = 4X + 3Y
iii) U(X, Y) = min(4X, 3Y)
Find the MRSxy for each of them and comment. Try to plot the indifference maps for these U-functions. Find the demand equations for X and Y for all the above i-iii curves using income I, price of X as Px and price of Y as Py. What about U(X, Y) = 4X - 3Y?
4. Sigit has the following utility function: U=x2/5y3/5 where x is his consumption of candy bars and y is his consumption of espressos. Given that utility function, his MUx = 2/5 x-3/5y3/5 and his MUy = 3/5 y-2/5x2/5. Use "I" for income.
a. Derive Sigit's demand curves for candy bars and espressos (note that a demand curve will be a function of Px or Py-given I.
b. Assume that Px = $1, Py = $2, and income I = $240. Draw his budget line. How many candy bars and espressos will Sigit consume? What is his level of utility at this amount?
c. Now suppose the price of espressos (y) goes up to $4, price of candy bars (x) and his income (I) remaining unchanged at part b. level. How many candy bars and espressos will Sigit consume? What is his level of utility at this amount?
d. What can you say about Sigit's preference from the above findings?
5)
a. Draw indifference maps to represent Ishita's preferences over the two commodities, x and y, in the following cases. What assumptions did you have to make? Comment on the MRSxy for each case:
i) x = money, y = air pollution.
ii) x = bitcoins, y = company shares; If a. Ishita does not like taking risk at all, b. Ishita really enjoys the thrills of taking risk and c. If Ishita likes to take risk but up to a certain limit beyond which she absolutely dislikes risks.
iii) x = 500g pack of sugar, y = 250g pack of sugar.
iv) x= waffles y = icecream; and Ishita will consume waffles (x) only with icecream (y).
v) x= electronic devices y= all other goods
Suppose the budget line is I = Px.X + Py.Y. Indicate on your maps where the utility maximizing solution will be reached for the 5 cases above.
b. For 5a.v, what happens to the budget line if the government applies a tax of $1 on the price of all electronic devices but does not tax other goods? What would be an "equivalent" income tax on your diagram?
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