Consider the following macroeconomic model: C(t) + I(t) = Y (t) I(t) = 0.8 dC(t) dt C(t) = 0.4Y (t) + 1 where C(t), I(t), Y (t) denote respectively the consumption, investment and national income at time t. Write the differential equation in terms of C(t), find the solution for the differential equation, and draw the phase diagram and comment on the stability.

For H₂O, determine the specified property at the indicated state.

(a) T = 140°C, v = 0.5 m³/kg. Find p, in bar.
(b) p = 30 MPa, T = 120°C. Find v, in m³/kg.
(c) p = 10 MPa, T = 450°C. Find v, in m³/kg.
(d) T = 80°C, x = 0.8. Find p, in bar, and v, in m³/kg.

Three people A, B, and C practice shooting at a target. The probability that A, B,
and C hit the target is 0.9, 0.8 and 0.6, respectively.
1) Now select any one of them at random, what is the probability that the person
selected hits the target?
2) If the person actually hit target, what is the probability that the person selected
is A?
3) If the person selected shoots once more, what is the probability that he hits the
target again?

We wish to estimate μ , the mean mass (in kg) of the Sandhill Crane. We take a random sample of 20 Sandhill Cranes and measure their masses. For this sample, we find an average mass of 4.53 kg and a standard deviation of 0.8 kg. Assuming the masses are normally distributed. Find the upper limits of 98% confidence interval for μ . Select the closest to your answer. options: 4.70 5.20 4.90 4.80 5.10 5.00

1. The consumer price index is a cost-of-living index.

False

True

2.Labor productivity is a major determinant of

the money supply.

the skill level of the labor force.

the size of the labor force.

living standards.

3.If consumption falls from $600 billion to $575 billion and the marginal propensity to consume is 0.8, then equilibrium income will

fall by $25 billion.

rise by $25 billion.

rise by $125 billion.

fall by $125 billion.

Tours Company Ratios:

Current Ratio = 1.30

Quick Ratio =  0.84

Average Collection Period =  72 Days

Fixed Assets Turnover =  1.15 times

Return On Equity = 0.142

The sector in which Tour operates has the following ratios:

Current ratio                           1.26

Quick ratio                              0.8

Average collection period      72

Fixed assets turnover ratio      1.10

Return on Equity                    0.45

Comment on the financial performance of Tours?

3. Due to political turbulences in Hong-Kong and the extensive protests consumers’ confidence
has deteriorated in the island. The marginal propensity to consume has declined from 0.8 to 0.6.

a. Use the consumption model to asses the effects of the decline in MPC on overall
consumption. Use the model and the graphs. Explain.

b. How it will affect overall aggregate demand? Use the AD model with positive slope (model, graph, and explanation).
(model, graph and explanation)

Use the table of standard normal probabilities (z table) to answer the following questions.

1. What is P(z >2.5)?
2. What is P(-0.8 < z < 1.5)?
3. What is P(0.65< z < 1.36)?  
4. What z-value leaves 80 % of the normal distribution to its right?
5. What z-value, and its negative, leaves 10 % of the normal distribution in each tail (a total of 20% of the distribution in both tails combined)?

1. If the MPC is 0.9, what is the size of the multiplier and the total change in real GDP demanded following a $1 billion decrease in spending?
2. If the MPC is 0.8, what is the size of the multiplier and the total change in real GDP demanded following a $1 billion increase in spending?
3. If the MPC is 0.75, what is the size of the multiplier and the total change in real GDP demanded following a $10 billion increase in spending?
4. What are the 3 main tools of monetary policy?