Illustrate the consumers budget line with lattes on the

Question

Can you help me with this question? Imagine a consumer with a weekly budget of $100, who faces prices of $5 for lattes and $1 for all other goods.

1. (a) Illustrate the consumer's budget line with lattes on the horizontal axis. Using an indifference curve, illustrate consumer's choice of 10 lattes.
2. (b) Suppose you observed that the consumer chose more lattes and fewer other goods when lattes went on sale. Can you infer whether the consumer's demand for lattes is elastic or inelastic from this choice? [Hint: Think about the relationship between elasticity and how total spending on a good changes.]
3. (c) Suppose instead that the price of lattes increases to $10. Illustrate the new budget line. Suppose the new consumption point is 4 lattes. Illustrate this new point with an indifference curve and explain the income and substitution effects of the price change assuming that lattes are a normal good. Is the consumer better or worse off after the price change?
4. (d) Assuming that the consumer's demand curve for lattes is linear, calculate and illustrate the change in consumer surplus from the price change.
5. (e) Now suppose that the consumer's favourite coffee shop offers a loyalty card for $20/week, which allows the purchase of lattes for $5 each. Will the consumer purchase the card?