Suppose that a firm’s production function is given by Q = ( K1/3 + L1/3 ) a , here α is a given parameter.(a) Find the marginal product of capital and labor.(b) Find the average product of capital and labor.(c) Does this production function have increasing, constant or decreasing re- turns to scale? Explain.(d) Find the marginal rate of technical substitution (RTS)(e) Use your result in (d) to find the elasticity of substitution.(f) Suppose a = 3. Set up the cost minimization problem of the firm and solve for the conditional demand for K and L

Use the following account numbers and corresponding account titles to answer the following question. account no. account title (1) cash (2) merchandise inventory (3) cost of goods sold (4) transportation-out (5) dividends (6) common stock (7) selling expense (8) loss on the sale of land (9) sales which accounts would appear on the income statement?

Lillypad toys is a manufacturer of educational toys for children. six months ago, the company's research and development division came up with an idea for a unique touchscreen device that can be used to introduce children to a number of foreign languages. three months ago, the company produced a working prototype, and last month the company successfully launched its new device on the commercial market. what should lillypad's managers prepare for next? a. increased competition from imitators b. a prolonged period of uncontested success c. a sharp decline in demand for the product d. a difficult struggle to move from invention to innovation

John and daphne are saving for their daughter ellen's college education. ellen just turned 10 at (t = 0), and she will be entering college 8 years from now (at t = 8). college tuition and expenses at state u. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. ellen should graduate in 4 years--if she takes longer or wants to go to graduate school, she will be on her own. tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and 11).so far, john and daphne have accumulated $15,000 in their college savings account (at t = 0). their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4). then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. they expect their investment account to earn 9%. how large must the annual payments at t = 5, 6, and 7 be to cover ellen's anticipated college costs? a. $1,965.21b. $2,068.64c. $2,177.51d. $2,292.12e. $2,412.76