4. We can express capital stock as a function of time: K(t). a. Express K(t) as the integral of the rate of net investment flow at time t, 1(t). Provide an economic interpretation of your result. b. Suppose I(t) = 3t0.5 and assume K(0) = c. Find the time path of capital.

Explain the difference between the stock variable and a flow variable in economics with one example of each.

A retired woman has $50,000 to invest but needs to make $6,000 a year from the interest to meet certain living expenses. One bond investment pays 15% simple annual interest. The rest of it she wants to put in a CD that pays 7% simple interest. a) Let x be the amount the woman invests in the 15% bond. Write an expression, in terms of x, that tells how much the woman invests in the CD. b) Set up an equation that can be used to determine how much the woman should invest in each option to earn $6,000 per year in interest. c) Solve the equation from part b) to determine how much should be invested in each option.

Suppose that the production function for an economy is given by Y = K1/4L3/4.  The depreciation rate is 4%, the saving rate is 12%, Show the steady state in a graph. In the same graph, show the effect of a decrease in the depreciation rate, say to 2%

In order to increase the creativity of its staff, Google invested in a highly uniqueheadquarters building, brimming with indoor leisure activities and places for staff tosocialize. What type of asset-specific investment is this?a. Site-specific investment.b. All other options are correct.c. Physical asset investment.d. Human asset investment.

Ecuador's economy has a production function that is as follows: Y = K2/5L3/5 The men in Ecuador generally stay home performing household chores while women work. Since the Ecuadorian state television stopped airing soap operas, many men decided to join the workforce and thus the labor force increased by 6.5%. However, recent storms have destroyed much of the capital stock of the country and thus the capital stock shrank by 2.5%. A. Assuming there is no change in total factor productivity in Ecuador, how would the output of Ecuador's economy change? B. How would labor productivity (output per worker) be affected by the increase in labor and decrease in capital stock? Explain. C. Assuming instead that Ecuador's economy grew by 4.9%, what would be the change in total factor productivity in the economy?

1.

Suppose that with all exogenous variables, including G and M at their original values, business becomes less confident about the future and reduce their autonomous level of investment from 500 to 200. Solve for the new values of e, Y and NX. With the help of graphs, explain very carefully the mechanisms by which a new equilibrium is reached.

A CES production function with physical and human capital Consider the CES production function in terms of physical capital, K, and human capital, H: where 0 a. Set up the Hamiltonian and find the first-order conditions. b. What is the optimal relation between K and H? Substitute this relation into the given production function to get a relation between Y and K. What does this “reduced-form” production function look like? c. What is the steady-state value of the ratio of physical to human capital, (K/H)∗? d. Describe the behavior of the economy over time if the initial condition is such that K(0)/H(0)? e. Suppose that the inequality restrictions IK ≥ 0 and IH ≥ 0 apply. How do these constraints affect the dynamics if the economy begins with K(0)/H(0)∗?

What is short-term momentum? What are long-term reversals?