You are given the following information for a closed economy in a general equilibirum context.

C^d = 5000 + 0.8Y - 80,000r , I^d = 1000 - 45,000r.

M^d/P = 0.9Y - 4000i ,  π ^e = 0.05, G = 450, Y-bar= 1000, and M = 3000.

a) Calculate the general equilibrium values of the real interest rate and the price level.

b) Explain what general equilibrium means in the IS-LM framework and how it is attained.

c) What kind of a shock has the Covid-19 pandemic crisis led to in the economies?

1. Consider the following equations that describe a closed economy with no government. Assume consumption is represented by the following: C = 200 + 0.9Y. Also assume that planned investment (I) equals 300.
   1. Obtain the saving function for this economy. What are the marginal propensity to save (MPS) and marginal propensity to consume (MPC)?
   2. Write the equation for the planned aggregate expenditure.
   3. Find the equilibrium level of output and calculate the level of consumption and saving that occurs at the equilibrium level of income.
   4. Explain the saving-investment approach to equilibrium. Recalculate the equilibrium level of output of the economy by saving-investment approach.
   5. Calculate the multiplier for this economy. Verbally explain the meaning of the calculated multiplier figure.
   6. Now, suppose the level of income is equal to 4000. What is the level of planned aggregate expenditures at this level of income? What is the value of any unplanned changes in inventories?
   7. Assume that investment increases by 25%. Using multiplier calculate the new equilibrium.

Consider a two-period model of a closed economy with government. Assume that the representative agent is endowed with ?1 and ?2 as initial endowments in period 1 and period 2 respectively, and has the utility function ? = ln ?1 + ? ln ?2, where ?1 and ?2 denote consumption and ? is the discount rate. Suppose that the government spends ?1 and ?2 in period 1 and period 2 and finances its expenditure through lump-sum taxes ?1and ?2 in periods 1 and 2 respectively.

(i) Derive the inter-temporal budget constraints of the representative agent and the government. [5]

(ii) Suppose if government borrows ? units at the interest rate of ? to finance its expenditure in period 1, derive the amount of taxes that would satisfy its inter-temporal budget constraint. Explain whether Ricardian Equivalence holds in this situation. [15]

IS-LM closed economy – SR

The Economy of North Haverbrook is described by the following agents and characteristics.

consumers C = 50 + 0.85 (Y-T)

(taxes) T = 100

(government expenditures) G = 100

(investments) I = 500 – 50r

(money supply) M = 3,000

(price levels) P = 1

(money demand) L (r,Y) = Y – 10r

(potential output) Y* = 3200

The goods and services markets in equilibrium is described as: Y = AE, where AE = C + I + G, and money market is in equilibrium when M/P = L(r,Y).

[2 points each, except for h) 4 points]

1. Find the aggregate expenditure function

2. Find the IS curve

3. Find the LM curve

4. Find the equilibrium exchange rate and output (Y, r)

5. Find the aggregate demand curve

6. Find Private savings, Public Savings and National savings

7. Do we have an expansionary gap or recessionary gap? What size?

8. If fiscal policy is used (government expenditure: G), how much +/- change will be required to close the gap?

1. If fiscal policy is not used, how will the gap close? (impact on prices and output – you can graph a diagram if it helps)

Suppose country Zee is a closed economy. Consider AD, SRAS and LRAS for the economy of Zee. Tye economy begins at price level P0, with output equal potential GDP=Y*, budget is balanced.

3.1 Suppose the government of Zee increases tax, T while keeping government expenditure G unchanged. Are we having budget deficit or surplus? What would be the effect of this action on loanable funds, real interest rate, private savings and investment, and levels of debt in country Zee?

3.2 Compare the short-run and the long-run effects of the governments policy stated in 3.1. Briefly mention what dilemma does the government face in implementing this policy.

We did an experiment : determination of entropy changes during melting of ice in a closed system. Can you write a 400 words paragraph introduction about The Second Law of Thermodynamics, entropy, entropy changes in reversible and irreversible processes, methods of calculating entropy changes in isothermal, isobaric and isochoric processes and entropy of the phase transformation.

In your own words. No copy-paste from the internet. Pleasee!!

A closed system contains an equimolar mixture of n-pentane and isopentane. a) Suppose the system is initially all liquid at 120°C and a high pressure, and the pressure is gradually reduced at a constant temperature. Estimate the pressures at which the first bubble of vapor forms and at which the last drop of liquid evaporates. Also calculate the liquid and vapor compositions (mole fractions) at those two conditions. b) Now suppose the system starts as a vapor at 1960 mm Hg and a high temperature, and the temperature is gradually reduced at constant pressure. Estimate the temperatures at which the first drop of liquid forms and at which the last bubble of vapor condenses. Also calculate the liquid and vapor compositions (mole fractions) at those two conditions. (use excel to solve question b.)

1.Suppose that the federal government has a budget deficit and the economy is closed. Using the savings–investment spending identity, explain how this affects investment spending.

2.The market for loanable funds is in equilibrium. All else equal, the federal government has eliminated taxes on interest earned from savings. Describe how this will affect the market for loanable funds, the equilibrium interest rate, and the equilibrium quantity of loanable funds.

Let (V, ||·||) be a normed space, and W a d^Norm_V,||·|| -closed vector subspace of V.

(a) Prove that a function |||·||| : V /W → R_≥0 can be consistently defined by ∀v ∈ V : |||v + W||| df= inf({||v + w|| : R_≥0 | w ∈ W}).

(b) Prove that |||·||| is a norm on V /W.

(c) Prove that if (V, ||·||) is a Banach space, then so is (V /W, |||·|||)

Let T be a connected graph and z ∈ℤ between the closed interval of 1 and the least degree of a vertex in T. Let a z - matching be a A ⊆ E s.t. there aren’t vertices with more than z edges in A. Let a z - cover be a X ⊆ E s.t. all vertices belong to at least z edges in X.

Let:

δ (T) = Max {|A| : A is a z - matching}

μ (T) = Min {|X| : X is a z - cover}

Show that δ (T) + μ (T) = zn