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.

When a metal object is dropped into cold water, it releases 4,715 J of energy to its surroundings, and its temperature decreases from [y].0 °C to 20.0 °C. The mass of the object is [x] grams. What is the specific heat of this material?

For the reaction Cl2 + 2 Br- → 2 Cl- + Br2, which of the following statements is NOT correct?

What volume in L of a 0.32 M Mg(NO3)2 solution contains [x] g of Mg(NO3)2 ? The molar mass of Mg(NO3)2 is 148.33 g/mol

What is the coefficient in front of the O2 when the equation below is balanced (using only whole numbers and the lowest whole number ratio)? C2H4(g) + O2 (g) → CO2(g) + H2O (g)

What is the mass, in grams, of [x] × 1021 silicon atoms?

Which picture BEST represents a mixture?  

Consider the following reaction: Mg2+(aq) + Cu(s) → Cu2+(aq) + Mg(s). In this reaction, Mg2+(aq) is: