1000 Lecture 10: Lec05 Subtense Bar (1)
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Units of X | MUx | Units of Y | MUy |
1 | 23 | 1 | 18 |
2 | 16 | 2 | 16 |
3 | 12 | 3 | 14 |
4 | 8 | 4 | 10 |
5 | 4 | 5 | 8 |
6 | 2 | 6 | 4 |
a. If your income is $9.00 and the prices of X and Y are $2.00 and $1.00, respectively, what quantities of each will you purchase to maximize utility? X = units. Y = units. b. What total utility will you realize?
c. Assume that other things remaining unchanged, the price of X falls to $1.00. What quantities of X and Y will you now purchase? X = units. Y = units.
d. Using the two prices and quantities for X derive a demand schedule (a table showing prices and quantities demanded) for X.
A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility that their consumption will yield is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend.
(a) Complete the following table by computing the marginal utility per dollar for successive units of X, Y, and Z to one or two decimal places.
(b) How many units of X, Y, and Z will the consumer buy when maximizing utility and spending all income? Show this result using the utility maximization formula.
(c) Why would the consumer not be maximizing utility by purchasing 2 units of X, 4 units of Y, and 1 unit of Z?
Product X | Product Y | Product Z | ||||||||
Quantity |
Utility |
Marginal Utility per $ |
Quantity |
Utility |
Marginal Utility per $ |
Quantity |
Utility |
Marginal Utility per $ |
||
1 | 42 | _____ | 1 | 14 | _____ | 1 | 32 | _____ | ||
2 | 82 | _____ | 2 | 26 | _____ | 2 | 60 | _____ | ||
3 | 118 | 3 | 36 | _____ | 3 | 84 | _____ | |||
4 | 148 | _____ | 4 | 44 | _____ | 4 | 100 | _____ | ||
5 | 170 | _____ | 5 | 50 | _____ | 5 | 110 | _____ | ||
6 | 182 | _____ | 6 | 54 | _____ | 6 | 116 | _____ | ||
7 | 182 | _____ | 7 | 56.4 | _____ | 7 | 120 | _____ |
Units of x | MUx | Units of y | MUy |
---|---|---|---|
1 | 23 | 1 | 18 |
2 | 16 | 2 | 16 |
3 | 12 | 3 | 14 |
4 | 8 | 4 | 10 |
5 | 4 | 5 | 8 |
6 | 2 | 6 | 4 |
You are choosing between two goods, X and Y, and your marginal utility from each is as shown above.
Instructions: Enter your answers as whole numbers.
a. If your income is $9.00 and the prices of X and Y are $2.00 and $1.00, respectively, what quantities of each will you purchase to maximize utility? X =___ units.Y =___ units.
b. What total utility will you realize? _______ .
c. Assume that other things remaining unchanged, the price of X falls to $1.00. What quantities of X and Y will you now purchase? X = __units. Y =__ units.
d. Using the two prices and quantities for X derive a demanding schedule (a table showing prices and quantities demanded) for X.
Price | Quantity demand |
? | ? |
? | ? |