Veena always consumes 3 times as much y as she consumes x. She will consume these goods in no other ratio. The price of x is three times the price of y. Veena has an endowment of 18 units of x & 78 units of y which she can trade at the ongoing prices. She has no other source of income. How much x will Veena buy from the market?
To determine how much x Veena will buy from the market, we need to understand her preferences and the prices of x and y.
Given that Veena always consumes 3 times as much y as she consumes x, we can express her consumption as follows:
y = 3x
We are also told that the price of x is three times the price of y. Let's assume the price of y is p, so the price of x would be 3p.
Next, let's compute the total value of Veena's endowment:
Value of x endowment = Price of x * Quantity of x = 3p * 18 = 54p
Value of y endowment = Price of y * Quantity of y = p * 78 = 78p
Since Veena has no other source of income, the total value of her endowment must be equal to the total value of the goods she consumes:
54p + 78p = Total value of her endowment
Now, we can solve for the value of p:
132p = Total value of her endowment
Given that Veena's endowment consists of 18 units of x and 78 units of y, we can compute the total value of her endowment:
Total value of her endowment = 18 * 3p + 78 * p
Setting the two equations for the total value equal to each other, we have:
54p + 78p = 18 * 3p + 78 * p
Simplifying the equation, we get:
132p = 54p + 234p
Combining like terms:
132p = 288p
Dividing both sides of the equation by 132, we find:
p = 0
This means that the price of y is 0. Since the price of x is three times the price of y, the price of x is also 0.
Therefore, with the price of both x and y being 0, Veena will not buy any units of x or y from the market.