Final answer:
When Lisa is given food coupons, her budget line will change, allowing her to purchase more food. When given cash instead of coupons, her budget line will not change. Depending on the shape of her indifference curves, Lisa may be indifferent between the two or prefer the cash transfer program.
Step-by-step explanation:
When Lisa is given $50 worth of food coupons, the coupons will alter her budget line by allowing her to purchase more food for the same amount of money. The slope of the budget line will be steeper, indicating that she can buy more food for every dollar spent.
When Lisa is given $50 in cash instead of coupons, her budget line will remain unchanged, as there is no alteration to her income or prices. The slope of the budget line will remain the same.
The economist friend's argument is that depending on the shape of Lisa's indifference curves, she could be indifferent between the food coupons and cash transfer program, or she could actually prefer the cash transfer program. If Lisa's indifference curves are relatively flat, indicating a low marginal utility of money, she may prefer the cash transfer program over the food coupons.
I have attached a diagram of Lisa's budget line and indifference curves to illustrate this argument.