The expression for total output and the dynamics of capital per worker are given by the following expressions: Y = AKᵃL¹⁻ᵃ Δk = sy - k , where A is the exogenous Solow residual, y is output per worker, and is the depreciation rate of capital.(a) Using the information given above, find the fundamental Solow equation. Find an expression for steady-state capital per worker. (b) What happens to steady-state capital if the depreciation rate goes up? (c) Suppose that this economy consists of two types of households: laborers and capitalists. Capitalists own all the capital stock K and are paid a rental rate equal to the marginal product of capital. Find an expression for their share of national income. (d) Assume that laborers save none of their income. If capitalists save 30% of their income, the parameter α = 0.3, and the parameter δ = 0.1, what is the aggregate saving rate s? Will income inequality between capitalists and laborers worsen over time?

Suppose you win a small lottery and have the choice of two ways to be paid: you can accept the money in a lump sum or in a series of payments over time. if you pick the lump sum, you get $2,950 today. if you pick payments over time, you get three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. 1) at an interest rate of 6% per year, the winner would be better off accepting the (lump sum / payments over time), since it has the greater present value. 2) at an interest rate of 9% per year, the winner would be better off accepting the (lump sum / payments over time), since it has the greater present value. 3) years after you win the lottery, a friend in another country calls to ask your advice. by wild coincidence, she has just won another lottery with the same payout schemes. she must make a quick decision about whether to collect her money under the lump sum or the payments over time. what is the best advice to give your friend? a) the lump sum is always better. b) the payments over time are always better. c) it will depend on the interest rate; advise her to get a calculator. d) none of these answers is good advice.

Why is it easier for new entrants to get involved in radical innovations when compared to incumbent firms? a. unlike incumbent firms, new entrants do not have to face the high entry barriers, initially. b. new entrants are embedded in an innovation ecosystem, while incumbent firms are not. c. unlike incumbent firms, new entrants do not have formal organizational structures and processes. d. incumbent firms do not have the advantages of network effects that new entrants have.

The following table gives the map coordinates and the shipping loads for a set of cities that we wish to connect through a central hub.,(7,(4,(7,(6,(2,( 2,) for the location of the proposed new central hub, the coordinates should be near: x==) if the shipments from city a double, for the location of the proposed new central hub, the coordinates should be near: x==.926.865.017.21