Question

1. A firm production function is given by q(l,k) = l^0.5·k^0.5, where q is number of units of output produced, l the number of units of labor input used and k the number of units of capital input used. This firm profit function is π = p·q(l,k) – w·l – v·k, where p is the price of output, w the wage rate of labor and v the rental rate of capital. In the short-run, k = 100. This firm hires its profit maximizing level of labor input. In the short-run, this firm demand equation for labor l is a factor a of (p/w)²: l = a (p/w)². In this specific case, factor a is equal to [a]. (HINT: This is unconstrained profit maximization problem. Set your first order condition by taking the derivative of your profit function with respect to l equal to zero, assume the second order condition is satisfied, and solve for l. NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero and trailing zeros when needed.)

2. An individual utility function is given by U(c,h) = c·h, where c represents consumption during a typical day and h hours of leisure enjoyed during that day. Let l be the hours of work during a day, then l + h = 24. The real hourly market wage rate the individual can earn is w = $20. This individual receives daily government transfer benefits equal to n = $100. For the graphical analysis of this individual’s utility maximization problem, consumption c is plotted on the vertical axis and hours of leisure h is plotted on the horizontal axis. The y-intercept for this individual’s full income constraint is [y]. (NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero and trailing zeros when needed.)

Answer 1