V+Consider a closed economy with fixed prices and wages. Suppose the consumption
function is given by
? = 50 + 0.5?
?
where C is consumption and ?
?
is disposable income. The investment function is
given by
? = 30 − 5?
where I is investment and r is the interest rate. The demand for money is given by
?/? = 200 + 2? − ℎ?
where M is the amount of money demanded, P is the price level, and h is a parameter
measuring the sensitivity of money demand to the interest rate. Assume that the
price level is fixed at P = 1.
(a) Assume that h=20. If government spending is G=20, taxes are T=10, and
the money supply is M=300, find the equilibrium levels of output and the
interest rate.

(b) Now assume that government spending decreases to 10. What is the
multiplier? Is the effect of government spending on output increased or
decreased when h is larger? Explain your answer intuitively.

(c) Now suppose taxes decrease to 0. What is the multiplier? Will the
multiplier be different than your answer in part (b)? Explain intuitively.

i am having trouble with b and c. could you do them in detail mainly the multipliers

In a closed economy, given the following:

The consumption function C = 0.8(1 – 0.25) Y + 12          

The average tax rate t = 25%

The level of private investment I = 26

The level of government spending G = 14

Where Y is the national income.

• Calculate the equilibrium level of income and output in the economy.
• Calculate the expenditure multiplier and show the effect of

1. an increase in government spending and
2. an increase in private investment.

Given the short run production function, Q = 3L2 – 0.1L3

( a) Write down the equations for,

(i) the marginal product of labor, MPL

(ii) the average product of labor, APL.

(b) Find the value of Q for which the MPL and APL are maximized.

(c) Show that the MPL= APL when the APL is at a maximum

A closed system consists of 0.5kg of superheated steam initially at 1MPa, 300 ⁰C. The system undergoes a reversible isothermal process during which the steam condenses to a saturated liquid whilst exchanging heat wih a reservoir at 30⁰C. Show the process on a T-s diagram and calculate the change in enthropy (kJ/K) of the system, the reservoir (surroundings) and the universe.

prove the sufficiency, let L be any closed contour in region R occupied by field A, suppose curl A=0 everywhere in R. then, since R is simply connected. L is the boundary of some surface S lying entirely in R. By Stoke's theorem, integral of A =0. prove that A is a potential field. ( potential and irrotational fields). please in details thx:)

2. Consider a domestic closed market (no international trade) with the following demand and supply functions:

P = 150 − 1/2Q

P=Q
(a) Calculate the domestic equilibrium price and quantity

(b) Calculate the consumer surplus and the producer surplus

(c) Suppose the domestic country decides to open up its markets and begins international trade. The world price (Pw) is $30 lower than the former domestic equilibrium price. How much quantity is now supplied by the domes- tic producers in the market? (QDomestic) How much quantity is imported from international producers in the market? (QImport). You must show work.

(d) (What is the new consumer surplus and producer surplus?

(e) Who benefited from opening up the market (Domestic consumers? Domestic producers?)

(f) (2 points) Did the domestic market efficiency improve?

Assume a closed economy without Government. However, there exists a financial sector that creates an array of financial assets on which both households and firms invest.

Let ? denote the average earnings from these financial assets. The consumption expenditure of the households is influenced by their wage income and the financial income and is given by ? = ?(?, ?); ?? > 0, ?? > 0, where ??, ?? are partial derivatives of consumption with respect to income ? and financial earnings ? respectively. Similarly, the real investment expenditure of firms is given by ? = ?(?, ?); ?? > 0, ?? < 0, where ??, ?? are the partial derivatives of the real investment with respect to income and financial earnings. Using either the Keynesian cross model or the Multiplier analysis, answer the following questions.

(i) Derive the relationship between output ? and financial earnings ?, and examine the analytical conditions under which the relationship is positive ( ?? ?? > 0) and negative ( ?? ?? < 0).

(ii) Describe why the scenario where the expansion in output driven by the rise in financial earnings, i.e. when ?? ?? > 0, could make the economy unstable and vulnerable to crisis?

Find a closed formula for each of the following sequences. Show all work and explain your answers.

(a) {1, 6, 17, 34, 57, 86, 121, . . .}, where a₀ = 1.

(b) a_n = 5a_n−1 + 4, a₀ = 2

(c) a_n = 10a_n−1 − 21a_n−2, a₀ = 6, a₁ = 26.

There are three possibilities for the shape/curvature of the universe: positive curvature (closed), negative curvature (open), and flat curvature. These all imply different things about the ultimate fate of the expanding universe. What kinds of observable tests could cosmologists use to distinguish one curvature from the next? Please write a detailed paragraph explaining what kinds of theory/observations cosmologists would have to make to determine that the universe has negative curvature (open)?