Core concept questions Question 1 Suppose that a rm produces output with capital and labor. Suppose that the production function is given by: Ma an=kh As usual, at denotes the wage rate, '1' denotes the rental price of capital, p denotes the price of output, and ydenotes the rm's target output level. Suppose that w = 1, r = 1, p = 1. We assume that factor markets are perfectly competitive (the factor supply functions are perfectly elastic). We also assume that the rm faces a perfectly competitive output market. 1. Set up and solve the rm's one step prot maximization problem. Obtain the rm's labor and capital demand, the rm's output, and its prots. 2. Set up and solve the rm's cost minimization problem. Find the rm's conditional labor and capital demands, minimum cost, and marginal cost if the rm must produce the output in part (1) at minimum cost. 3. Plot the solution to the cost minimization problem making sure that you label all important components of your plot. Plot the isoquant in red and the isocost line in blue. 4. Set up and solve the rm's two step prot maximization problem. Plot your solution in price output space. Draw the price line in black and marginal cost in red. Make sure you label everything clearly. Question 2 Consider a monopoly that has a constant cost function given by: 0(9) = 631- Let market demand be given by the linear function: 1100) = a bp- 1. What is the monopolist's objective function? 2. What is the monopolist's output and price? 10. 11. 12. . In a graph, plot market demand, marginal cost, and marginal revenue. . Label the monopoly quantity, 9"", and the monopoly price pm. . In the gure from part (4), shade the monopoly prots in red and the monopoly's total cost in blue. Shade consumer surplus in green. . Suppose, now, that the total cost function was the industry cost function. What is the industry supply function? . In a graph, plot market demand and industry supply. . Find the competitive quantity and price and label them (1'3 and 19\