ECO 3152 Lecture Notes - Lecture 5: Budget Constraint, Competitive Equilibrium, Real Wages

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16 Nov 2018

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Closed economy - model of a single country that has no interaction with the rest of the world: no trade. Three different actors in the economy: representative consumer, representative firm, the government. Wants to purchase a given quantity of consumption goods (g), and finances these purchases by taxing the representative consumer Fiscal policy - refers to the governments choices over its expenditures, taxes, transfers and borrowing. Exogenous variables -> consumption, labor supply, labor demanded, taxes, wage, aggregate output. Given market prices, demand is equal to supply in each market in the economy --> competitive equilibrium: all consumers and firms are price takers, all actions of all consumers and firms are consistent. When demand = supply in all markets market clearing. Our model economy: one price (real wage, one market, labor time is exchanged for consumption goods, representative consumer supplies labor and the rep firm demands labor.

Related Questions

Let us have an economy that lives only for 2 periods. The representative household has a utility function that values consumption goods for any period as follows

u(c) = ln(c).

The valuation throughout both periods can be represented as a total utility function that discounts future utility with a Î² discount parameter as follows,

U(c1, c2) = u(c1) + Î²u(c2) = ln(c1) + Î² ln(c2),

where ct represent consumption good in period t for every period t = 1, 2. The budget constraint for this person in every period is expressed as

(1+Ïtc)ct + xt =(1âÏtI)(wtnt +rtkt), t=1,2.

where xt represent investment in period t, wt the wages earned by hours worked, rt the return of capital in period t, nt the hours worked supplied by the household in every period t, kt the stock of capital that the household has in period t, Ïtc the tax rate imposed by the government in consumption goods in every period t, and ÏtI the tax rate imposed by the government to total household income in every period t. In every period, the total amount of hours that the representative household is of H Ì = 1. Investment in every period can be defined by the following law of motion of capital

kt+1 = xt +(1âÎ´)kt, t=1,2.

Acknowledge that k3 = 0 because there is no period 3 in this economy. The household starts with a given amount of capital k Ì1 > 0. The representative firm produces good by the following production function in every period t,

Y_t =z_tK_tÎ±N_t1âÎ±, t=1,2.

There is a government that covers government expenditures in period 1 and period 2 by taxing capital rent and labor. Hence, their budget can be expressed as

Ïtcct +ÏtI(wtnt +rtkt)=gt, t=1,2.

a) Before writing any competitive equilibrium definition or the Social Planner Problem, can we modify the budget constraint in â¨order to get rid a variable in every period? Explain.

b) Define the Social Planner Problem.

c) Solve the Social Planner Problem. This is, find the Euler equation in terms of exogenous variables and the only endogenous variable k2.

d) Define the tax distorted competitive equilibrium of this economy.

e) Solve the representative household problem.

f) Solve the representative firm problem in period 1 and 2.

g) Find the optimal Euler equation in terms of exogenous variables and the only endogenous variable k2.

h) Imagine that the government can only implement income taxes. This is Ïtc = 0 for every period t = 1, 2. Can the government implement a tax plan that achieves the Pareto allocation reached by the Social Planner Problem?

i) Imagine that the government can only implement consumption taxes. This is ÏtI = 0 for every period t = 1,2. Can the government implement a tax plan that achieves the Pareto allocation reached by the Social Planner Problem? â¨

Country A is located on a small island that is isolated from the outside world. The country
has one representative consumer, whose preference is represented by:
U(c, l) = ln(c) + ln(l)
There is one representative fi rm in the economy which is owned by the consumer, it produces
one type of good that can be used for consumption or government expenditure using capital
and labour as inputs. The fi rm owns the capital it uses and it's production technology is
represented by
F(K;N) = zK^aN^1-a
where z is the total factor productivity, and a is the capital share of income. The fi rm pays
all of its profit back to consumer as dividend.
The government of country A spend a predetermined G amount of goods to provide public
services, and it taxes consumer through a lump-sum tax t to finance the expenditure. the
government's budget is balanced:
G = t
Now, suppose that the firm cannot change its capital stock, or improve its production technology in the short period, such that z and K are given.
(a) When describing this economy as an macroeconomic model, what is the set of exogenous
variables? What is the set of endogenous variables that can be determined given the set
of exogenous variables using the concept of Competitive Equilibrium?
(b) Defi ne the competitive equilibrium for this economy, be specific about what it is, what
conditions have to be satisfied who solves what problem and etc.
(c) List the set of equations that will be used to determine all of the endogenous variables.
Which four of these endogenous variables are essentials, such that once you know these
four, all other endogenous variables can be obtained easily?
(d) Write down the four equations that can be used to solve for these four essential endogenous variables, and describe where do they come from. Describe in details the steps of
how would you solve for the competitive equilibrium (without actually solving for it ).
(e) Setup the Social planner's problem for this economy. What is the marginal condition
that pins down the planner's choices.
(f) Now, describe what would happen to c, l, and w if the firm had more capital, such
that Knew > Kold.

10.

The long-run aggregate supply curve (LRAS) is Y = Yf, which depends on the amounts of resources and the level of technology innovation. If a country has more resources and better technology, which of the following is true?

		A. The LRAS curve will shift to the right.
		B. The SRAS will shift to the right.
		C. The SRAS will shift to the left.
		D. Only A and B.
		E. Only A and C.

11.

Suppose the wage rates of workers are based on the expected price level. If there is an unexpected increase in AD, it will cause the actual price level to increase. Then workers should raise their expected price level and negotiate a higher wage rate. Then which of the following is most likely to be true when the expected price increases?

		A. The SRAS curve will shift rightward.
		B. The SRAS curve will shift leftward.
		C. The LRAS curve will shift leftward.
		D. Only A and C.
		E. Only B and C.

12.

Suppose the economy is in the long-run equilibrium, i.e., Y = Yf, and there is an unexpected decrease in AD. Assume that Yf is fixed, then which of the following is most likely to be true?

		A. The SRAS curve will shift to the right toward the new long-run equilibrium.
		B. The SRAS curve will shift to the left toward the new long-run equilibrium.
		C. In the new long-run equilibrium, price level will be higher.
		D. Only A and C.
		E. Only B and C.

13.

The short-run (SR) equilibrium is the intersection between AD and SRAS, and long-run (LR) equilibrium is the intersection between AD and LRAS. Every LR equilibrium is a SR equilibrium, but a SR equilibrium is not always the LR equilibrium. If an economy is operating at a SR equilibrium where Y > Yf, which of the following will occur in the process toward the new LR equilibrium when the economy corrects itself?

		A. Price increases.
		B. Real GDP decreases.
		C. Unemployment rate falls.
		D. Only A and B.
		E. Only B and C.

14.

From the Keynesians, Y = C + I + G + NX can be transformed into a theoretical model. In particular, assume that the consumption C = A + mpc (Y-T), where A is a constant, mpc is the marginal propensity to consume, Y is national income and T is income taxes. Suppose in the goods market equilibrium, aggregate expenditure = national income such that the two Y's will be the same from Y = A + mpc (Y-T) + I + G+ NX. . Suppose C = 400 + 0.75(Y â T). G = 100, I = 100, T = 100, and NX = 150, what is the Y in the goods market equilibrium? (All of the variables are in terms of million dollars)

$ million
Please enter a whole number, with no decimal point.

15.

Continue to assume that C = 400 + 0.75 (Y - 100), I = 100, and NX = 150. But the government now increases spending from 100 to 200, how much is the new Y in the goods market equilibrium?

$ million
Please enter a whole number, with no decimal point.

16.

Continue to assume that C = 400 + 0.75 (Y - 100). Then which of the following is true?

		A. The government spending multiplier = 4.
		B. The tax multiplier = 3.
		C. If the government increases spending by $50 million, and at the same time increases taxes by $50 milion to balance the budget, AD will shift to the right by $50 million.
		D. Only A and C.
		E. Only B and C.

17.

Suppose the federal government needs to balance the budget, which means that when the government spending increases, taxes must increase equally. In this case, government spending multiplier is called the balanced-budget multiplier, defined as the increase in real GDP/increase in government spending. By following the example from the previous question, how mcuh is the balanced-budget multiplier?

Please enter a whole number, with no decimal point.

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ECO 3152 Lecture Notes - Lecture 5: Budget Constraint, Competitive Equilibrium, Real Wages

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