q = K^1/2 L^1/2 p=$20, v=$8, w=$4
a) suppose k= 16, find short-run total and marginal costs, and also firm supply function. Find the price that the firm shuts down its production.
b) find firm profit maximization demand function and short-run supply function
In: Economics
For the ellipse 6? 2 + 4? 2 = 36, find the eccentricity and sketch the graph showing all main features including axis intercepts, foci and directrices.
b) Using exclusively some part of your answer to part a), determine the foci and directrices for the curve: (? + 2) 2 6 + (? − 3) 2 9 =
In: Math
Suppose that a 2 × 2 matrix A has eigenvalues λ = -3 and 4, with corresponding eigenvectors [1m1]and [7,2], respectively. Find A^2.
In: Math
Given the data below for the reaction, 2 A + 2 B + 4 C => D + E + 3 F,
| Experiment | Initial conc of A, mol/L | Initial conc of B, mol/L | Initial conc of C, mol/L | Initial rate, mol/L.s |
| 1 | 0.1 | 0.2 | 0.4 | 2 x 10-3 |
| 2 | 0.2 | 0.2 | 0.4 | 4 x 10-3 |
| 3 | 0.3 | 0.4 | 0.4 | 6 x 10-3 |
| 4 | 0.4 | 0.6 | 0.2 | 2 x 10-3 |
Calculate the value of k to 3 significant figures.
In: Chemistry
Consider the following function ?(?) = ?^ 4+ 2? ^3 + 8?^ 2+ 5? With the initial guesses of ?1 = −2, ?2 = −1, and ?3 = 1, find the minimum of the given function using parabolic interpolation. Perform five iterations, reporting Ɛa based on the location of the minimum (i.e. xopt) and not the actual minimum value. (Round the final answer to four decimal places.)
In: Advanced Math
Show that ? = {1 − ?, 2 + ?2, 1 + ? − ?2} forms a basis for ?2(ℝ)
In: Math
For the following exercises, use the given information about the polynomial graph to write the equation.
Degree 4. Roots of multiplicity 2 at x = 1/2 and roots of multiplicity 1 at x = 6 and x = −2. y-intercept at (0,18).
In: Advanced Math
1.What is the coordination number for each of the following complexes?
[Co(NH3)4Cl2]+
[Pb(EDTA)]2?
[Cu(NH3)4]2+
[Ag(NH3)2]NO3
2.What is the charge on each of the following complex ions?
hexaaquachromium(II), [Cr(H2O)6]?
tris(carbonato)ferrate(III), [Fe(CO3)3]?
diaquatetrabromovanadate(III), [V(H2O)2Br4]?
3.What is the oxidation number of the central metal ion in each of the following complexes?
[NiCl2Br2]2?
[Fe(H2O)2(NH3)4]3+
Na[Rh(CN)2]
In: Chemistry
Given the following Cobb-Douglas production functions:
F(L,K) = LK^2
F(L,K) = L^3/4K^1/4
F(L,K) = L^1/2K^1/4
1. Determine the returns to scale for each function.
2. For the rest of this exercise assume that the price of labor, w,
and the price of capital, r,
equal 1: w = r = 1. Find the conditional input demand functions of
labor and capital (the
cost-minimizing combinations of labor and capital).
3. Now find the cost functions for each of the production
functions.
4. For each of the above production functions, functions, plot the
cost function on the same
graph with Q on the horizontal axis and total cost on the vertical
axis.
5. Find and plot the average and marginal cost functions with Q on
the horizontal axis and
average cost on the vertical axis. Related these graphs with your
answers to the returns to
scale of the production function you found in subquestion 1.
In: Economics
Production Function:
| Labor (L) | 1 | 3 | 6 | 10 | 15 |
| Total Product (Q) | 1 | 2 | 3 | 4 | 5 |
1. Using the data in the table above, compute the marginal product using the definition given earlier in this module. Draw a graph of the marginal product curve using the numbers you computed. Suppose this firm can hire workers at a wage rate of $10 per hour to work in its factory which has a rental cost of $100. Use the data in the table above to calculate the costs (i.e., a data table showing costs at various levels of production) in the following steps:
2. First compute the variable cost for Q = 0 through Q = 5.
3. Next compute the fixed cost for Q = 0 through Q = 5.
4. Then compute the total cost for Q = 0 through Q = 5. This is the cost function.
5. Finally compute the marginal cost for Q = 0 through Q = 5. Draw the marginal cost curve and compare it to the marginal product curve above. Explain what you see.
In: Economics