Analytic Question on Consumption and Labor decisions during the Pandemic . In this question we will study how workers change their labor supply. Imagine there is a consumer/worker with preference over consumption C and leisure & given by the equation below: U(C, l) = log(C) + log(l) 1. Assume the consumer faces wage w and consumption prices P. She also has one unit of available time to spend working or resting. Solve for the consumer problem by choosing hours worked and consumption. Compute the elasticity of consumption with respect to real wages. 2. Now assume there is a shopping spree in the economy, wherein the consumer receives more utility from consumption. We model this by changing the preferences to: U(C,1)= y log(C) + log(l) with 1. Solve for the hours worked and consumption under this new assumption. Compare your answer with the previous part (where = 1). Does the consumer wants to work more or less? 3.The government fears that a virus will spread in the population, so it decides to limit the number of hours the consumer can work. We model this by assuming that the maximum hours worked can be , with 0<<< . With words, explain why the optimal hours worked for the consumer will be h = C. Solve for consumption and leisure, given h = 5. 4. Now imagine that after the government's new regulation occurs, a new form of work becomes available to the consumer. We assume she can work online with no restrictions because the government has no control on online hours worked. Explain why the new budget constraint can be written as: PC = wt (1-o-l) +woo, where we is the wage in the traditional sector, w, is the wage in the new online sector and o are the hours worked online. Assuming wo < wt < w (¹+c), explain why the consumer would choose to work as many hours as possible in the traditional sector and the remaining hours they work online. 5. Following part d, solve for the hours worked in both sectors and the total hours worked. Does this new form of work improve consumption? Compare consumption with part c. 6. Following part d, what would be the optimal labor restriction ? Explain your answer based on the First Welfare Theorem, assuming the prices clear markets in a competitive equilibrium.