Final answer:
Emilio's budget constraint will experience a parallel outward shift if her income increases to $110 or the price of pizza decreases to $8.
Step-by-step explanation:
A budget constraint shows the combinations of goods that a consumer can afford to buy given their income and the prices of the goods. In this case, we are considering Emilio's budget constraint for pizza and soda. To determine if the budget constraint will experience a parallel outward shift, we need to analyze each event:
a) If Emilio's income increases to $110, the budget constraint will shift outwards in a parallel manner because Emilio will be able to afford more pizza and soda.
b) If the price of pizza decreases to $8, the relative price of pizza compared to soda decreases, causing the budget constraint to rotate outwards. This will lead to Emilio being able to afford more pizza and soda.
c) If the price of soda increases to $3, the relative price of soda compared to pizza increases, causing the budget constraint to rotate inwards. As a result, Emilio will be able to afford less pizza and soda.
d) If Emilio receives a $20 gift card for pizza, it does not affect her income or the prices of pizza and soda. Therefore, the budget constraint will not shift and remain the same.
Based on this analysis, events a) and b) will result in a parallel outward shift of Emilio's budget constraint.