In this question we will study how workers change their labor supply. Imagine there is a consumerfworker with preference over consumption C and leisure If given by the equation below: 01 U(c, f?) = log{c) + log{) . Assume the consumer faces a wage rate of w and consumption price P. She also has one unit of available time to spend working or resting. Their budget constraint is Pc = w {1 E) . Solve for the consumer's optimal choice of consumption and hours worked. . Now assume a pandemic hits the economy and the consumer receives more utility from leisure. W'e model this by changing the preferences to: U(c, E] = log{c) + 310g() with 9 > 1. Solve for the hours worked and consumption under these new preferences. Compute the elasticity of labor supply and consumption with respect to real wages. Compare your answer with the previous part (when 3 = 1). Does the consumer wants to work more or less? . The government wants to increase hours worked, and so it enacts a law that includes a subsidy on wages. This subsidy is proportional to labor income. Explain why the new budget constraint can be expressed as: Pr: = {1 + r)w{1 E), where 1- is the subsidy (with r > 0). Solve for the optimal hours worked and consumption and compare your answer with that of the previous question. What is the effect of this subsidy on hours worked? . Now the government wants to try a different scal policy. Instead, it creates a new lump-sum tax that the consumer has to pay regardless of income or consumption. Explain why the new budget constraint can be written as: Pa = w(1 E) T, where T is the new lump-sum tax. Assume 0