1. Craig spends his entire budget. He can just a8ord 10 apples and 7 pears. He c
ID: 1173968 • Letter: 1
Question
1. Craig spends his entire budget. He can just a8ord 10 apples and 7 pears. He can also just aeord 20 apples and 2 pears. If income is 12, then what is the price of an apple? (a) 1 (b) 2 (c) .50 (d).75 (e) none of the above. 2. Assume that px and py 2. What is utility as a function of income for utility u(x;y2y for income m larger than 1 (a) 2m i (b) 2m +,2 (c) mi (d) m+ (e) m t 3. David has utility function U(x;y)-minf3x;3yg. He has 13 units of good x and 9 units of y. Aner's utility function for the same two goods is U(xy) 2x +2y. Aner has 6 units of x and 15 units of y. The current allocation is (a) Pareto optimal and envy free (neither envies the allocation of the other). (b) Not Pareto optimal and not envy free. (c) Pareto optimal and not envy free. (d) Not Pareto optimal and envy free. (e) Since they have diCerent preferences, there is not enough information to determine the answer 4. One can prove that the following utility u(x;y)- x2+4y is not homothetic with the following example a (1;2) b (2:1) and (a) k il (b) k 1-4 (c) k 2 (d) There is no k such that this example will work. It would require dier- ence choices of a and b. (e) One can't come up with a counter example since the utility is homo- thetic.Explanation / Answer
Question 1
Craig can afford 10 apples and 7 pears.
He can also afford 20 apples and 2 pears.
This means if he has to increase his consumption of apples by 10 units, he has to sacrifice consumption of pears by 5 units.
Slope of budget line = Quantity of pears sacrificed/Quantity of apples gained = 5/10 = 0.5
Slope of budget line can also be stated as follows -
Slope of budget line = Price of apples/Price of pears
So,
Price of apples/Price of pears = 0.5
Price of apples = 0.5Price of pears
Income is $12.
So, when Craig consumes 10 apples and 7 pears, budget equation can be written as follows -
(10 * Price of apples) + (7 * Price of pears) = 12
(10 * 0.5Price of pears) + 7Price of pears = 12
5Price of pears + 7Price of pears = 12
12Price of pears = 12
Price of pears = 12/12 = 1
Price of apple = 0.5Price of pears = 0.5 * 1 = 0.50
Thus,
The price of apples is 0.50
Hence, the correct answer is the option (c).
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