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All of the following questions in the space given below each question
All of the following questions in the space given below each question. This question is worth 5 Marks You are choosing between two goods, X and Y marginal utility from each is as shown in the table below. If your income is $36 and the prices of X and Y are $8 and $4, respectively then use the table below to answer the following questions Units of X Total Marginal $/Mux Units of Y Total Marginal S/Muy Utility Utility of X Utility Utility of Y 1 1 32 2 32 2 28 3 28 3 24 4 16 4 20 5 12 5 16 6 4 6 8 . Fall in the table abc What quantities of X & Y will you purchase to maximize total utility? What will be the maximum total utility? Assume that other things remain unchanged, the price of X falls to $4. What quantities of X and Y Will you purchase now? Using the two Prices and quantities of X derive the demand curve for good X
Expert Solution
| Units of X | TU | MUx | MU$x | MU$x1 | Units of Y | TU | MUy | MU$y |
| 1 | 44 | 44 | 5.5 | 11 | 1 | 32 | 32 | 8 |
| 2 | 76 | 32 | 4 | 8 | 2 | 60 | 28 | 7 |
| 3 | 104 | 28 | 3.5 | 7 | 3 | 84 | 24 | 6 |
| 4 | 120 | 16 | 2 | 4 | 4 | 104 | 20 | 5 |
| 5 | 132 | 12 | 1.5 | 3 | 5 | 120 | 16 | 4 |
| 6 | 136 | 4 | 0.5 | 1 | 6 | 128 | 8 | 2 |
Total Utility (TU) = summation of MU
MU per dollar (MU$x) = MU / price of x
MU per dollar (MU$y) = MU / price of y
1. Budget constraint: $8x + $4y = $36 where x = units of x and y = units of y
The income will be spent according to descending order of the MU$.
According to law of equi marginal utility, that combination of two goods should be purchased where the marginal utility of dollar from last units of both goods is equal to each other. Keeping total income in mind, this will happen at x=2 units and y=5 units. Here, MU$x = MU$y = 4.
Total utility will be maximized when 2 units of X and 5 units of Y are bought. This also satisfies the budget constraint as $8*2 + $4*5 = $36.
2. Maximum total utility = total utiltiy at 2 units of X + total utility of 5 units of Y
Maximum total utility = 76 + 120 = 196
3. When price of X falls to $4, new MU$x is has been calculated in MU$x1 column.
New budget constraint: $4x + $4y = $36 where x = units of x and y = units of y
According to law of equi marginal utility, that combination of two goods should be purchased where the marginal utility of dollar from last units of both goods is equal to each other. Keeping total income in mind, this will happen at x=4 units and y=5 units. Here, MU$x = MU$y = 4.
Now total utility will be maximized when 4 units of X and 5 units of Y are bought. This also satisfies the budget constraint as $4*4 + $4*5 = $36.
4. Taking price on y axis and quantity bought on x axis, the demand curve for x can be derived.
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