6. Baskets of almonds and pecans are bought and sold in a well-functioning market that is in equilibrium. One basket contains 20 almonds and 20 pecans while the second basket contains 10 almonds and 40 pecans. Both baskets are priced at $15. To preclude arbitrage, what is the price of a basket that contains 24 almonds and 16 pecans? a.$20 b.$18 c.$16 d. It would not have a unique price e. None of the above
Question
- Baskets of almonds and pecans are bought and sold in a well-functioning market that is in equilibrium. One basket contains 20 almonds and 20 pecans while the second basket contains 10 almonds and 40 pecans. Both baskets are priced at 20 b.16 d. It would not have a unique price e. None of the above
Solution
To solve this problem, we first need to determine the price of a single almond and a single pecan.
From the first basket, we know that 20 almonds and 20 pecans cost 15/20 = $0.75.
From the second basket, we know that 10 almonds and 40 pecans cost 15/10 = $1.50.
From these two pieces of information, we can set up a system of equations to solve for the price of a single almond (A) and a single pecan (P):
1A + 1P = 1.50
Solving this system of equations, we find that A = 0.25.
Therefore, a basket that contains 24 almonds and 16 pecans would cost 24A + 16P = 24(0.25) = 4 = $16.
So, the answer is c. $16.
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