**Consumer Equilibrium in Case of Two Commodities**

Consumer equilibrium refers to the condition where a consumer maximizes their satisfaction or utility by allocating their limited income among different goods and services. In the case of two commodities, the consumer has to make choices regarding the quantities of each commodity to purchase in order to achieve the highest level of satisfaction.

To solve questions based on consumer equilibrium in the case of two commodities, we can use the concept of marginal utility and the budget constraint. This analysis involves comparing the marginal utility per unit of money spent on each commodity and adjusting the quantities until the consumer reaches equilibrium.

**Step 1: Determining Marginal Utility**

- Calculate the marginal utility (MU) of each commodity by taking the derivative of the utility function with respect to the quantity of that commodity consumed. The utility function represents the consumer's preferences and satisfaction.
- For example, if the utility function for commodity X is U(X) = X^0.5, where X represents the quantity consumed, then the marginal utility of X (MUx) would be MUx = (0.5)X^(-0.5).

**Step 2: Determining the Marginal Utility per Unit of Money Spent**

- Calculate the price ratio (Px/Py) of the two commodities, where Px is the price of commodity X and Py is the price of commodity Y.
- Calculate the marginal utility per unit of money spent on each commodity by dividing the marginal utility of a commodity by its price.
- For example, if MUx = (0.5)X^(-0.5) and Px = $2, then the marginal utility per dollar spent on X (MUx/Px) would be (0.5)X^(-0.5)/$2.

**Step 3: Equating Marginal Utility per Unit of Money Spent**

- Set the marginal utility per unit of money spent on each commodity equal to each other (MUx/Px = MUy/Py) to determine the optimal quantities of each commodity.
- Rearrange the equation to solve for the quantity of one commodity in terms of the other.
- For example, if MUx/Px = MUy/Py, and Py = $3, then rearranging the equation would give (0.5)X^(-0.5)/$2 = MUy/$3.

**Step 4: Determining the Optimal Quantities**

- Substitute the value of the unknown quantity from the rearranged equation into the budget constraint equation (PxX + PyY = I), where I represents the consumer's income.
- Solve the equation for the remaining unknown quantity.
- For example, if the budget constraint is $10 = $2X + $3Y, substitute the value of X from the rearranged equation into this budget constraint equation to solve for Y.

**Step 5: Checking for Consumer Equilibrium**

- Calculate the total utility (TU) by plugging the values of X and Y into the utility function.
- Compare the TU obtained with other possible combinations of X and Y within the budget constraint to identify the combination that maximizes utility.
- If the TU obtained is the highest among the feasible combinations, then the consumer has reached equilibrium.

By following these steps, one can solve questions based on consumer equilibrium in the case of two commodities. It is important to note that the utility function, prices, and income may vary in different scenarios, so it

We can solve the question by putting their values than by solving it we see which one is greater than we increase the consumption of greater one then law of DMU applied then we attain equilibrium.