5. A consumer can spend her fixed income of $200 on two products, food (F) and luxuries, (L). The consumer's tastes are represented by the utility function U = FL. Food sells for $2 per unit and luxuries sell for $5 per unit.

a. Draw the budget constraint of the consumer and explain your diagram.

b. Knowing that the marginal utilities of F and L are MUF = L and MUL = F, respectively, compute the amount of each good in the consumer's optimal basket.

c. Assume that the government adds a tax of $1 to the price of luxuries. How does it affect the optimal consumption of the individual?

d. Calculate the income and substitution effects on the consumption of luxuries after the increase in their prices due to the tax. Draw a graph illustrating these effects.