Consider a static (one-period), closed economy with one representative consumer, one rep- resentative firm, and a government. The level of capital K and government expenditures G in the economy are both fixed exogenously. The government levies a lump sum tax T in order to fund its purchases, and the government budget must balance. Suppose the price of consumption is normalized to one (p = 1). The representative consumer has 24 hours of time available each day (h = 24), which she can use only for labor or leisure. She receives labor income, profits from the firm (), and pays lump sum taxes (T). The consumer's utility function is u(c, 1) = ln(c) + ln(1), and the firm's production function is Y =zK N. 1. (4 points) List the requirements that must be satisfied to achieve competitive equilibrium in this economy. = 3 2. (6 points) Suppose z = 6, 0 K = 8, and the hourly wage is w = 8. Solve the firm's profit maximization problem for N*. Compute the firm's output Y and profit at the optimal choice of N*. = 48 3. (6 points) Suppose the consumer earns hourly wage w = 8, pays lump-sum taxes T per day, and receives the profits from the firm that you found in part 2 above. Solve for the consumer's optimal choices c* and l*, and determine how much labor the consumer supplies. 4. (4 points) Write the market clearing equations for the output and labor markets. State whether or not these markets clear, i.e. whether or not supply equals demand in each. [Note that G = 48 since T = 48 and the government budget must balance.] If the markets do not clear, state whether there is excess demand or excess supply in each market. 5. (5 points) This economy is not in equilibrium, and in order to achieve equilibrium the wage rate would need to adjust. Would the wage would need to increase or decrease to achieve equilibrium? Why? Your explanation should include a description of how both consumer and firm behavior would change, and why those changes would move the economy towards equilibrium. [Hint: your explanation should include discussion of each of the endogenous elements in the market clearing equations from part 4.] 6. (3 points (bonus)) Find the equilibrium wage rate that would satisfy competitive equilib- rium in this economy. Show that the output and labor markets clear at the wage rate that you found. (Note: the solution for w* is not a whole number, so you should round to two decimal places in all calculations.)