Question
When a consumer is in equilibrium, $MRS_{XY}$ is 2.5. If the price of commodity Y is 16, then what will be the price of commodity X ?
The correct answer is
40
Equilibrium Condition & Calculation
A consumer is in equilibrium when the ratio of the marginal utility of two commodities equals the ratio of their prices. Mathematically, this is represented as:
$ MRS_{XY} = \frac{P_X}{P_Y} $
Where:
- $MRS_{XY}$ is the Marginal Rate of Substitution of commodity X for commodity Y.
- $P_X$ is the price of commodity X.
- $P_Y$ is the price of commodity Y.
Solving for Price of Commodity X
We are given:
- $MRS_{XY} = 2.5$
- $P_Y = 16$
Substitute these values into the equilibrium condition:
$ 2.5 = \frac{P_X}{16} $
To find the price of commodity X ($P_X$), rearrange the equation:
$ P_X = 2.5 \times 16 $
Calculate the result:
$ P_X = 40 $
Therefore, the price of commodity X is 40.
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