During the pandemic people spent more time consuming home-cooked meals (ql) as opposed to eating out at restaurants (qr2 ). Suppose the average price of a home cooked meal was p1 = 20, the price of eating out was p2 = 15 , and average spending was $300 per week. The typical consumer picks ql and q2 to maximize utility function U = (110.5qu subject to their budget. 1. (4 points) Based on the Lagrangian problem done in class (and in the book), write out the general consumer demand functions that we found for q, and q2 and then calculate what these are for the situation described ab0ve. How many meals are eaten at home versus out per week? 2. (4 points) Write out the budget constraint. Then, write it in a form that is good for graphing, meaning that q2 is an the left-hand side. Then, solve for the horizontal intercept (i.e., solve for q] when 9'2: 0) and the vertical intercept (i.e., solve for q2 when q1= O). 3. (3 points) Graph the budget constraint and show the initial equilibrium where consumption occurs, with ql on horizontal axis and q2 on the vertical axis. Draw an indifference curve (in a general shape that is consistent with the utility function described above) that is tangent to the budget constraint at the consumption point you found in problem 1. 4. (3 points) Now suppose the price of home cooked meals (P1) declines while p2 and Yremain as in problem 1. Create a graph that shows both the original and new budget lines and indifference curves. Demonstrate how the curves or lines shift or rotate. Then, draw a Price Consumption Curve, that is, the line through the optimal bundles. Consider whether it is at, upward sloping, downward sloping, or something else. (Look in the notes and book if you're not sure.)