Problem 1: \"To work, or not to work\" A consumer has preferences described by the utility function u(c,l) = Inc 7h, where c denotes consumption, h 6 {0,1} is indisible labor, and qr > 0 is a parameter- Assume that the total number of hours available to the consumer is H = 1. The consumer receives the hourly wage to for rendered labor services. b A. Obtain the labor supply curve. (Hint: You need to calculate the reservation wage 11.13. See relevant slides for the denition of reservation wage.) B. Introduce a proportional tax on labor income, 7w, so that the after-tax wage is if: E (1 Tw)w. Obtain the new labor supply curve. How does the labor supply curve change when we increase Tm? Explain. C. Introduce a proportional tax on consumption, 1}. Obtain the new labor supply curve. How does the labor supply curve change when we increase Tc? Explain. Problem 2: \"To shop, or not to shop\" A consumer has preferences described by the utility function u(c,q) = inc + (19, where c denotes \"necessity\" consumption (food), q 6 {0,1} denotes \"luxury\" consumption (cars), _ and a > 0 is a parameter. Cars are an indim'sz'ble good, so that you either buy it, or you do not. The price of food is equal to 1, whereas the price of a car is p. The consumer has income to. A. Solve for the optimal demand of food (3\" and cars q\". B. Introduce a proportional tax on the purchase of cars, Tq, so that the price of a car becomes p E (1 + 79);). Obtain the new demand curve for cars. How does the demand for cars change when we increase 713 Explain