Information for questions 5-7 The following figure shows three isoquants for a firm that produces candy, with units of labor on the horizontal axis, and units of capital on the vertical axis. Each isoquant is labeled with the output of candy that its combinations of labor and capital produce. Note that each grid spacing is 0.25 on both axes. Also shown are some auxiliary lines in solid black. The steepest line has slope = 2, and the three flattest lines all have slope = 1 (all of these slopes are in absolute value). Note that each of the auxiliary lines is tangent to an isoquant, and that its tangency point is marked with a dot.   Starting from the wage of w=50 and the rental rate of r=25, suppose that the rental rate increases to 50. Calculate the change in the amount of capital that the firm employs, in order to keep producing 15 units of candy at minimum cost. This can be an increase or a decrease, make sure to enter a positive number for an increase, and a negative number for a decrease.

Information for questions 16-17 A firm has short-run production function given by . Note that in the short run, we can replace K in the production function f(L,K) by whatever constant value K has in the short run, and so the production function becomes effectively only a function of L. Here, the firm is using 10 units of capital in the short-run. This firm’s short-run (total) cost function is given by .   Calculate the rental rate. Only the exact answer is accepted. Write 0 if the exact answer cannot be calculated with the information given.

Information for questions 13-19 The following figure shows the cost curves for a firm in a perfectly competitive market. Only exact answers are accepted. For numeric questions, enter 0, if the question cannot be answered with the information provided. In particular, since the figure does not have a grid, do not try to approximate any numbers using its scale. You can only use the numbers provided on the figure to perform an exact calculation. If you feel that an exact calculation is not possible for a given question, then the correct answer would be 0, or “none of the above.”   For the first three questions in this group, the firm is operating in the short run.   For the firm to make positive profits, the market price must exceed:

Information for questions 34-40 The figure shows the Demand curve for a monopoly. This monopolist has no fixed cost, and a constant Marginal Cost = 0.5 (the Marginal Cost curve is also shown). Note that one horizontal grid space = 5 units, while one vertical grid space = $0.25. For all numeric questions, only the the exact answer will be accepted. Adhere to the following convention, which is necessary to get exact answers: if a line seems to cross an intersection of the grid, then by convention assume that it does. For example, the choke point of the demand curve seems to be where P=3, Q=0, so assume that that is the exact choke point, that is, that when the price P=3, then the demand is Q=0, exactly. If a question cannot be answered with the information given, enter the number 0.   Calculate the profit per unit that the monopolist makes. Note: if the profit per unit is a loss, enter a negative number.

Information for questions 29-33 Suppose that demand for a monopolist is given by Q = 4000 – 500 P. The monopolist’s total cost function is given by C = 180 + 5.5Q + Q2/2000. Calculate the monopolist’s profit. Only exact answer accepted. Enter 0, if the answer cannot be obtained with the information given.

Information for questions 10-12 A firm’s short-run total cost function is given by C=550 + 300 Q + 10 Q2. Capital is the only input that is fixed in the short run, that is, it cannot be changed in the short run. Labor, on the other hand, is variable, and can be changed in the short run. The rental rate is $25 per unit of capital, the wage is $50 per unit of labor. For this group, answers within 1% of the correct answer are accepted, so carry several decimals in your calculations. Enter 0 if the question cannot be answered with the information provided.   How many units of capital is the firm using, in the short run?

Information for questions 4-8 The following figure shows three isoquants for a firm that produces chocolate, with units of labor on the horizontal axis, and units of capital on the vertical axis. Each isoquant is labeled with the output of chocolate that its combinations of labor and capital produce, in tons of chocolate. Note that each grid spacing is 0.25 on both axes. Also shown are some auxiliary lines in solid black. The steepest line has slope =1, and the three flattest lines all have slope = 1/3 (all of these slopes are in absolute value, by the way). Note that each of the auxiliary lines is tangent to an isoquant, and that its tangency point is marked with a dot. For the numerical answers, only exact answers are accepted. For that purpose, adopt the convention: if a line seems to cross a grid point, assume that it does so exactly. For example, the Q=20 isoquant ends at point (L=8, K=1), exactly. Suppose that the wage is 10 and rental price is also 10. What is the minimum cost for the firm to produce 20 tons of chocolate?

Information for questions 9-12 The following are some equations that may be useful for this group of questions. They assume that we graph isoquants and isocost lines with labor on the horizontal axis, and capital on the vertical axis. In all cases, “slope” refers to the absolute value of slopes that may actually be negative. Marginal Product of Labor:

Information for questions 10-12 A firm’s short-run total cost function is given by C=550 + 300 Q + 10 Q2. Capital is the only input that is fixed in the short run, that is, it cannot be changed in the short run. Labor, on the other hand, is variable, and can be changed in the short run. The rental rate is $25 per unit of capital, the wage is $50 per unit of labor. For this group, answers within 1% of the correct answer are accepted, so carry several decimals in your calculations. Enter 0 if the question cannot be answered with the information provided.   At what production level Q does the firm minimize its Average Cost?

Information for questions 4-8 The following figure shows three isoquants for a firm that produces chocolate, with units of labor on the horizontal axis, and units of capital on the vertical axis. Each isoquant is labeled with the output of chocolate that its combinations of labor and capital produce, in tons of chocolate. Note that each grid spacing is 0.25 on both axes. Also shown are some auxiliary lines in solid black. The steepest line has slope =1, and the three flattest lines all have slope = 1/3 (all of these slopes are in absolute value, by the way). Note that each of the auxiliary lines is tangent to an isoquant, and that its tangency point is marked with a dot. For the numerical answers, only exact answers are accepted. For that purpose, adopt the convention: if a line seems to cross a grid point, assume that it does so exactly. For example, the Q=20 isoquant ends at point (L=8, K=1), exactly. Starting from a wage of 10 and a rental price of 10, suppose that the rental price increases to 30. Calculate the change in the amount of labor that the firm employs, in order to keep producing 20 tons of chocolate at minimum cost. Note that this change can be an increase in the amount of labor, or a decrease, so remember to enter the right sign: that is, enter a positive number if the firm increases the amount of labor, and a negative number if the firm decreases the amount of labor.