Px = 2.00 Py = 1.00 Income = $12.00. Quantity table with values for Mux and Muy for quantities 1 through 8.

• Price of Good X ($\text{P}_x$) = $2.00
• Price of Good Y ($\text{P}_y$) = $1.00
• Income = $12.00

We calculate $\frac{\text{MU}_x}{\text{P}_x}$ and $\frac{\text{MU}_y}{\text{P}_y}$ for each quantity (Q).

The equilibrium condition is $\frac{\text{MU}_x}{\text{P}_x} = \frac{\text{MU}_y}{\text{P}_y}$. We look for quantities where these values are equal and then check if the total cost equals the income of $12.00.

• If $\frac{\text{MU}_x}{\text{P}_x} = \frac{\text{MU}_y}{\text{P}_y} = 8$:

  • $\text{Q}_x = 1$, $\text{Q}_y = 4$
  • Cost = $(1 \times$2) + $(4 \times$1) = $2 +$4 = $6.00 (Less than income)

• If $\frac{\text{MU}_x}{\text{P}_x} = \frac{\text{MU}_y}{\text{P}_y} = 7$:

  • $\text{Q}_x = 2$, $\text{Q}_y = 5$
  • Cost = $(2 \times$2) + $(5 \times$1) = $4 +$5 = $9.00 (Less than income)

• If $\frac{\text{MU}_x}{\text{P}_x} = \frac{\text{MU}_y}{\text{P}_y} = 6$:

  • $\text{Q}_x = 3$, $\text{Q}_y = 6$
  • Cost = $(3 \times$2) + $(6 \times$1) = $6 +$6 = $12.00 (Exactly equals income)

• If $\frac{\text{MU}_x}{\text{P}_x} = \frac{\text{MU}_y}{\text{P}_y} = 5$:

  • $\text{Q}_x = 4$, $\text{Q}_y = 7$
  • Cost = $(4 \times$2) + $(7 \times$1) = $8 +$7 = $15.00 (Exceeds income)

The consumer equilibrium occurs when the consumer purchases 3 units of Good X and 6 units of Good Y, as this combination satisfies both the equal marginal utility per dollar condition and the budget constraint.

The consumer's new equilibrium point is:

• Quantity of Good X: $\boxed{3 \text{ units}}$
• Quantity of Good Y: $\boxed{6 \text{ units}}$