1 Preference change Consider a one-period closed economy, i.e. agents (consumers, firms and government) live for one period, consumers supply labor and demand consumption good, whereas firms supply consumption good and demand labor, and government finances an exogenous spending via lump-sum taxes. Suppose that representative consumer's preferences change, in that n goes up. 1. How does the marginal rate of substitution of leisure for consumption change for each value of consumption and leisure? (MRS.c) 2. Interpret what this change in preferences means in more intuitive language. 3. Analyze the effects of this change in preferences on the consumption/leisure choice of the individuals given a constant wage and tax. Support your answer with appropriate graphs. 4. How does this change affect the labor supply curve. (Ns(w)) Where; We have the time constraint | + NS = 1For the following questions, consider a partial equilibrium environment where a consumer makes "consumption-leisure" choice and a firm makes production decisions. All prices (like the wage rate w) and policies (like consumption tax " or labor tax rate 7 ) are taken as given when the agents make their optimal choices. To do the analysis in this homework, you need to know some technical assumptions. The con- sumer's static utility function is in the form of U(c, () = log(c) +7log(1). c is the final consumption and / is the amount of leisure time. Here, the parameter 7 indicates how much he/she cares about leisure or "utility weight of leisure". Suppose people's total hour endowment is 1. So we have the time constraint / + /$ = 1. In addition to the wage income, the consumer are also shareholder's of the firm. So he/she gets the after tax profits. The firm has a Cobb-Douglas production function that transforms capital and labor into final consumption good: Y = F(K, N*). Given this is a static problem, there is no investment and capital K is held as constant. We assume the consumer always maximizes his/her utility under the budget constraint and the firm always optimizes its profits given its technology (production function). Go to Settings to activate Windows