i) State the conditions to be satisfied for consumer’s equilibrium under cardinal
and ordinal approach.
(ii) What is production possibility curve (PPC)? How does a PPC provide an
economy’s menu of choices? 

(i) Conditions for Consumer's Equilibrium under Cardinal and Ordinal Approach

1. Cardinal Approach to Consumer’s Equilibrium:
In the cardinal approach, consumer equilibrium is based on the idea of measurable utility (in units). This approach was developed primarily by economists like Alfred Marshall. A consumer attains equilibrium when they maximize total utility given their budget constraint. The key conditions for consumer equilibrium under the cardinal approach are:

- Law of Diminishing Marginal Utility: The marginal utility (MU) of a good decreases as more units of the good are consumed.
  
- Equalization of Marginal Utility per Dollar Spent (Law of Equi-Marginal Utility): A consumer should allocate their budget in such a way that the last unit of money spent on each good provides the same level of marginal utility. Mathematically, it is expressed as:

  \[
  \frac{MU_x}{P_x} = \frac{MU_y}{P_y}
  \]

  Where:
  - \(MU_x\) and \(MU_y\) are the marginal utilities of goods \(x\) and \(y\), respectively.
  - \(P_x\) and \(P_y\) are the prices of goods \(x\) and \(y\), respectively.

  This means that for equilibrium, the ratio of the marginal utility of a good to its price should be the same for all goods. If this condition is not met, the consumer can reallocate their expenditure to get a higher total utility.

- Budget Constraint: The consumer's total expenditure on goods should not exceed their income. This can be expressed as:

  \[
  P_x \times X + P_y \times Y = M
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