Problem 5, 6, 7

Problem 5: A student consumes two goods, books (B) and coffee (C) each month. Her utility function is: U(B,C) = 5 302 Her monthly budget for books and coffee is $90. A. If books cost $15 and coffee costs $3, What is her optimal consumption bundle per month? (Use the Lagrangian method). B. Graph her budget line, indifference curve and optimal bundle of books and coffee. C. Find and interpret the value of it. D. Conrm that MRS = MRT: Problem 6: Burger Patch customers see some items as substitutes and others as complements. Given the scenarios below, give the utility function and derive the demand function. Use income = Y. A. The secret menu has a myriad of loaded fry options. In winter, customers perfectly substituted between the chili patch spuds (C) and the loaded shovel (L) in a 1-to-1 ratio, assume pc = pL=p. B. A shake (S) is the perfect complement to a Burger Patch burger (B). In fact, every two burgers are complemented with one shake. C. The price of a BP shake is $5.90 and 3 Patch Burger is $7.90. What is the income elasticity of demand for shakes at Y = $100? Plot the Engel curve for shakes. Problem 7: Each week, Marie stocks up on her favorite snacks: dark chocolate (D) and popcorn (P). Her snack budget is $201week. Her consumption the rst week of June was D1 = 5 and P' = 5. The initial prices of Marie's snacks are p}, = $1 and p}, = $3. During the second week of June, the price of popcorn increased to $4. In response to this, Marie decreased her conSUmption of popcorn in week 2 to P2 = 3 and spent the rest of her budget on chocolate. How much would Marie need to increase her snack budget to continue to consume the same amount of chocolate and popcorn as in week 1? Illustrate on a graph the total effect, income effect and substitution effect of the price increase in popcorn (no specic values needed)