Question

Competitive Equilibrium (10 pts) Consider an economy with a representative consumer, a representative firm, and a government.

• The consumer can work up to h hours at an hourly rate of w. She only gets utility from consumption and does not care about how much she works. Their preferences are represented by the utility function U(C, l) = ln(C). The consumer also owns an exogenously given K units of capital, which they can rent to the firms at a price r, and which is taxed by the government at rate τ . The consumer’s budget constraint is therefore: C ≤ wNs + (1 − τ )rKs + π where Ns = h − l is the amount of labor the consumer chooses to supply, Ks is the amount of capital the consumer chooses to sell, and π is the profit of the firm. The consumer treats both τ and π as given.

• The firm operates using a CRS technology that uses labor and capital to produce. Total output is Y = zF(Kd , Nd ) = z · Kd α · Nd 1−α , where Kd is the capital demanded by the firm, Nd is the labor demanded by the firm, and the exponent α is some constant between 0 and 1. The firm must pay w for each unit of labor, and r for each unit of capital. The firm seeks to maximize profits, choosing capital and labor demand.

• The government has an exogenously given amount of spending, G, which must be funded. The only tax they collect is an ad valorem tax on capital rent at a rate τ . Government revenue is τ rKs . The main change from what we worked with in class is that here, the consumer owns the initial stock of capital, and that taxes are collected on capital income rather than being lump-sum or collected on labor income. -

1. Define an equilibrium for this economy. Make sure to specify all the relevant problems and conditions.

2. Find the labor and capital supply. Draw them in two diagrams. (If you draw these by hand, neatly label them and scan the images, or attach the page with your drawings to the homework. But hint: these graphs should be very easy to draw, even on a computer.)

3. Pose the firm’s problem and get the firm’s FOC. What are firm’s profits in equilibrium?

4. Define what it means for an equilibrium of THIS economy to be Pareto efficient.

5. Pose the planner’s problem for this economy. Interpret the planner’s constraints.

6. Is the equilibrium Pareto efficient? Show why or why not using the planner’s problem

Answer 1

What is Economic Equilibrium?

Economic equilibrium is a condition or state in which economic forces are balanced. In effect, economic variables remain unchanged from their equilibrium values in the absence of external influences. Economic equilibrium is also referred to as market equilibrium.

Economic equilibrium is the combination of economic variables (usually price and quantity) toward which normal economic processes, such as supply and demand, drive the economy. The term economic equilibrium can also be applied to any number of variables such as interest rates or aggregate consumption spending. The point of equilibrium represents a theoretical state of rest where all economic transactions that “should” occur, given the initial state of all relevant economic variables, have taken place.

Types of Economic Equilibrium

In microeconomics, financial balance may likewise be characterized as the cost at which supply equivalents interest for an item, as it were the place the theoretical organic market bends cross. On the off chance that this alludes to a business opportunity for a solitary decent, administration, or factor of generation it can likewise be alluded to as incomplete harmony, rather than general balance, which alludes to a state where all last great, administration, and factor markets are in balance themselves and with one another all the while. Harmony can likewise allude to a comparative state in macroeconomics, where total stock and total interest are in equalization.

Market interest, in financial aspects, connection between the amount of an item that makers wish to sell at different costs and the amount that purchasers wish to purchase. It is the principle model of value assurance utilized in monetary hypothesis. The cost of a product is dictated by the communication of organic market in a market. The subsequent cost is alluded to as the harmony cost and speaks to an understanding among makers and buyers of the great. In balance the amount of a decent provided by makers approaches the amount requested by customers.

2.Request Bend

The amount of a product requested relies upon the cost of that item and possibly on numerous different variables, for example, the costs of different wares, the livelihoods and inclinations of purchasers, and occasional impacts. In essential financial investigation, all components aside from the cost of the product are frequently held steady; the examination at that point includes looking at the connection between different value levels and the most extreme amount that would conceivably be acquired by shoppers at every one of those costs. The value amount mixes might be plotted on a bend, known as an interest bend, with cost spoke to on the vertical hub and amount spoke to on the level hub. An interest bend is quite often descending slanting, mirroring the ability of shoppers to buy a greater amount of the item at lower value levels. Any change in non-value elements would cause a move in the interest bend, while changes in the cost of the ware can be followed along a fixed interest bend.

Supply Bend

The amount of an item that is provided in the market depends not just on the value reachable for the ware yet additionally on conceivably numerous different components, for example, the costs of substitute items, the generation innovation, and the accessibility and cost of work and different variables of creation. In fundamental monetary examination, investigating supply includes taking a gander at the connection between different costs and the amount conceivably offered by makers at each value, again holding consistent every single other factor that could impact the cost. Those value amount blends might be plotted on a bend, known as an inventory bend, with cost spoke to on the vertical hub and amount spoke to on the even pivot. A stockpile bend is typically upward-slanting, mirroring the eagerness of makers to sell a greater amount of the product they produce in a market with more significant expenses. Any change in non-value variables would cause a move in the stockpile bend, while changes in the cost of the item can be followed along a fixed inventory bend.

Market Balance

It is the capacity of a market to compare request and supply through the value component. On the off chance that purchasers wish to buy to a greater extent a decent than is accessible at the predominant value, they will in general offer the cost up. On the off chance that they wish to buy not exactly is accessible at the predominant value, providers will offer costs down. Subsequently, there is a propensity to advance toward the balance cost. That propensity is known as the market component, and the subsequent harmony among organic market is known as a market balance.

As the cost rises, the amount offered typically increments, and the ability of purchasers to purchase a decent regularly decreases, yet those progressions are not really corresponding. The proportion of the responsiveness of market interest to changes in cost is known as the value versatility of stock or request, determined as the proportion of the rate change in amount provided or requested to the rate change in cost. In this manner, if the cost of a product diminishes by 10 percent and offers of the item thus increment by 20 percent, at that point the value versatility of interest for that ware is said to be 2.

The interest for items that have promptly accessible substitutes is probably going to be versatile, which implies that it will be progressively receptive to changes in the cost of the item. That is on the grounds that buyers can undoubtedly supplant the great with another if its value rises. The interest for an item might be inelastic if there are no nearby substitutes and if consumptions on the item establish just a little piece of the customer's salary. Firms looked with generally inelastic requests for their items may build their absolute income by raising costs; those confronting versatile requests can't.

Organic market investigation might be applied to business sectors for definite merchandise and ventures or to business sectors for work, capital, and different components of generation. It very well may be applied at the degree of the firm or the business or at the total level for the whole economy.

3.Absolute Income and Complete Cost Approach: A firm is said to be in harmony when it boosts its benefit. It is the moment that it has no inclination either to increment or agreement its yield.

States of the Balance of Firm:

A firm is said to be in balance when it fulfills the accompanying conditions:

1. The primary condition for the balance of the firm is that its benefit ought to be greatest.

2. Minimal expense ought to be equivalent to negligible income.

3. MC must cut MR from underneath.

The above states of the balance of the firm can be analyzed in two different ways:

1. Complete Income and All out Cost Approach

2. Peripheral Income and Minimal Cost Approach.

1. Complete Income and All out Cost Approach:

A firm is said to be in harmony when it amplifies its benefit. It is the moment that it has no inclination either to increment or agreement its yield. Presently, benefits are the contrast between all out income and all out expense. So as to be in balance, the firm will endeavor to amplify the contrast between absolute income and all out expenses. It is obvious from the figure that the biggest benefits which the firm could cause will to be earned when the vertical separation between the all out expense and absolute income is most noteworthy.

Complete Income and All out Cost Approach

In fig. 1 yield has been estimated on X-pivot while value/cost on Y-hub. TR is the absolute income bend. It is a straight line bisecting the starting point at 45°. It implies that cost of the item is fixed. Such a circumstance exists just under immaculate challenge.

TC is the absolute cost bend. TPC is the all out benefit bend. Up to OM1 level of yield, TC bend lies above TR bend. It is the misfortune zone. At OM1 yield, the firm just takes care of expenses TR=TC. Point B shows zero benefit. It is known as the make back the initial investment point. Past OM1 yield, the contrast among TR and TC is certain up to OM2 level of yield. The firm makes greatest benefits at OM yield on the grounds that the vertical separation among TR and TC bends (PN) is most extreme.

The digression at point N on TC bend is parallel to the TR bend. The conduct of complete benefits is appeared by the specked bend. All out benefits are most extreme at OM yield. At OM2 yield TC is again equivalent to TR. Benefits tumble to zero. Misfortunes are least at OM] yield. The firm has crossed the misfortune zone and is going to enter the benefit zone. It is implied by the make back the initial investment point-B.

2. Negligible Income and Minor Cost Approach:

Joan Robinson utilized the apparatuses of negligible income and peripheral expense to show the harmony of the firm. As per this technique, the benefits of a firm can be assessed by ascertaining the minor income and peripheral expense at various degrees of yield. Minimal income is the distinction made to add up to income by selling one unit of yield. Also, peripheral expense is the distinction made to add up to cost by delivering one unit of yield. The benefits of a firm will be most extreme at that degree of yield whose peripheral expense is equivalent to minor income.

In this manner, each firm will expand yield till negligible income is more noteworthy than minor expense. Then again, if peripheral expense happens to be more prominent than negligible income the firm will support misfortunes. In this manner, it will be in light of a legitimate concern for the firm to get the yield. It very well may be appeared with the assistance of a figure. In fig. 2 MC is the upward inclining negligible cost bend and MR is the descending slanting minimal income bend. Both these bends cross each other at point E which decides the Bull level of yield. At Bull level of yield peripheral income is simply equivalent to minor expense.

That is to say, firm will boost its benefits by delivering Bull yield. Presently, if the firm delivers yield less or more than Bull, its benefits will be less. For example, at OX1 its benefits will be less in light of the fact that here MR = JX1, while MC = KX1 In this way, MR > MC. In a similar manner at OX2 level of yield peripheral income is not exactly minimal expense. In this manner, past Bull level of yield additional units will add more to cost than to income and, in this way, the firm will acquire a misfortune on these additional units.

Other than first condition, the subsequent request condition should likewise be fulfilled, in the event that we need to be in a steady balance position. The subsequent request condition requires that for a firm to be in harmony minimal cost bend must cut negligible income bend from underneath. On the off chance that, at the purpose of balance, MC bend cuts the MR bend from above, at that point past the purpose of correspondence MC would be lower than MR and, thusly, it will be in light of a legitimate concern for the maker to grow yield past this fairness point. This can be clarified with the assistance of the figure.

In figure 3 yield has been estimated on X-hub while income on Y-pivot. MC is the minimal cost bend. PP bend speaks to the normal income just as minor income bend. It is obvious from the figure that at first MC bend cuts the MR bend at point E1. Point E1 is known as the 'Equal the initial investment Point' as MC bend converges the MR bend from above. The benefit boosting yield is OQ1 on the grounds that with this yield minimal expense is equivalent to negligible income (E2) and MC bend meets the MR bend from underneath.

A. Assurance of Short Run Harmony of Firm:

Short-run alludes to that period wherein fixed components staying unaltered the organizations so as to cause most extreme benefits can differ their yield by changing the variable elements like work, crude material and so on. In the brief time frame, it isn't fundamental that the organizations must win super­normal or typical benefits however even the organizations may need to support the misfortunes.

A firm may gain supernormal benefits on the grounds that in the short run, firms can't enter the business. Besides, a firm may endure misfortunes, in light of the fact that in the short run, may not step up generation in any event, when cost of the item falls. On the off chance that, it stops creation briefly, it should bear the loss of fixed cost which will establish the base misfortunes of the firm.

Nonetheless, all the above expressed potential outcomes have been clarified as under:

(I) Supernormal Benefits:

A firm is said to be in harmony when its negligible expense is equivalent to peripheral income and minor cost bend cuts the minimal income bend from underneath. A firm in harmony appreciates supernormal benefits if normal income surpasses minimal expense. This reality has been appeared in fig 4.

In figure 4 yields has been appeared on level hub and income on vertical pivot. MC and air conditioning are the negligible expense and normal cost bends individually. PP is the normal income bend. It is obvious from the figure that MC bend converges the MR bend from beneath at point N which shows yield Bull. At this degree of yield cost is NX and normal expense is MX. Since normal income is more prominent than normal cost, the firm is gaining super-ordinary benefits MN per unit of yield. Consequently, the absolute super-typical benefits of a firm will be equivalent to PLMN.

(ii) Ordinary Benefit:

Ordinary benefits allude to those benefits where the normal expense of the firm equivalents the normal income. These benefits spread only the reward for innovative administrations and are incorporated into the expense of creation. It very well may be appeared with the assistance of a figure. In figure 5 the balance has been portrayed at point E. At point E minimal income is equivalent to negligible expense and peripheral expense meets the minor income bend from underneath. The firm wins ordinary benefits at Bull yield on the grounds that at this yield both the states of balance are satisfied.

(iii) Least Misfortunes:

A firm in balance acquires misfortunes when it doesn't take care of the normal expense. As it were, when normal income misses the mark concerning normal cost, the firm needs to continue misfortunes. In figure 6 the firm is said to be in balance at point T. At this degree of yield both the states of harmony are fulfilled i.e., minimal income is equivalent to minor expense and negligible cost bend converges the peripheral income bend from beneath. Therefore, it decides the Bull level of yield correspondingly cost is Operation. It implies misfortune per unit of yield is RT. Along these lines, misfortunes will be PSTR.

Assurance of Short Run Harmony of Firm

(iv) Shut Down Point:

Basic inquiry is the reason firms keep creating the item on the off chance that they are making misfortunes. In the short run, the organizations can't leave the business by arranging off the plant. For what reason do they not shut down? It is on the grounds that they can't change the fixed components and they need to face fixed expenses regardless of whether the firm is closed down.

The firm can keep away from just factor costs yet it needs to hold up under the fixed costs whether to deliver or not. The firm will keep creating till the value takes care of the normal variable expense. On the off chance that the value covers some piece of the normal fixed costs other than the variable costs, the maker will keep delivering. Accordingly the firm will keep creating insofar as value surpasses normal variable expense. The shut down point can be appeared with the assistance of a graph.

Close Down Point

In graph 7 harmony is at E where MR = MC and MC cuts MR from underneath. The cost is EQ and OQ is the yield. This value takes care of the normal variable expense. Normal cost relating to this yield is AQ. In that manner misfortune per unit is AE which is equivalent to average fixed expense. The complete misfortunes are equivalent to add up to fixed expenses. In the event that cost is somewhat beneath Operation, level, the firm won't create by any stretch of the imagination. The firm will just close down creation and hang tight for some great days to come.

Close Down Point (Losses=Total Fixed Expenses):

Be that as it may, the firm may keep on working even under such a circumstance due to the accompanying reasons:

1. The firm may keep on working in light of the fact that a higher valuation (esteem) is given to an on­going concerns instead of a shut down firm.

2. More renown is appended to the proprietor or administrator of an on-going worry than to that of a firm that has shut down or stopped to work.

3. By propping the activity up, the firm won't lose skillful faculty.

4. The firm may keep on working in the expectation of gaining benefits in future.

B. Assurance of Since a long time ago Run Balance of the Firm:

Since a long time ago run alludes to that period wherein the maker can change its stock by changing every one of the variables of generation. At the end of the day, the maker has the adequate time to alter their provisions as indicated by the changed interest conditions.

Additionally, new firms can likewise enter and existing firms can leave the business. Over the long haul, the firm is said to be in harmony when minor expense is equivalent to cost. Other than it, the firm under ideal challenge to be in harmony cost must be equivalent to average expense. For the most part, over the long haul, firm in harmony acquires typical benefits. In the event that the organizations happen to gain the overly ordinary benefits in the significant stretch, the current firms will build their generation.

Baited by excessively typical benefits some new firms will go into the business. The absolute stock of the item will increment and the value tumbles down. In this manner, because of fall in value the organizations will get typical benefits. On the off chance that cost of the item is not exactly the normal cost, the organizations would make misfortunes. These misfortunes would instigate a few firms to leave the business. Thus the yield of the business will fall which will raise the value, henceforth, the organizations will start to gain typical benefits. It very well may be appeared with the assistance of a figure 8.

In figure 8 yield has been delineated on X-hub while income on Y-pivot. SAC is the short run normal cost bend and LAC is the since a long time ago run normal cost bend. Thus, SMC and LMC are the short run minimal expense and since quite a while ago run negligible cost bends individually.

Give us a chance to assume that the business decides Operation cost. At this value firms are delivering with SAC1 and is acquiring too typical benefits equivalent to the concealed zone PLNM. Attracted by these overly typical benefits, the current firms will expand their creation limit, in this manner, the new firms will enter the business. Because of the section of the new firms supply of the item will build which will prompt a fall in cost.

Assurance of Since quite a while ago Run Harmony of the Firm

Along these lines, the cost will tumble to Operation'. At this value, the firm will be in harmony at point E and will deliver OQ level of yield. It is because of the explanation that at point E, minor income, since quite a while ago run minimal cost, normal income and since a long time ago run normal expense are for the most part equivalent and the firm acquires typical benefits.

Emblematically:

MR = LMC = AR = LAC = SAC = SMC = Cost

Challenges of TR-TC Approach:

The principle troubles of TR and TC approach are as under:

1. It is hard to break down at what level of yield benefits are most extreme.

2. It is hard to see initially the most extreme vertical separation among TR and TC approach.

3. It is hard to find the value per unit of yield.

Harmony of Industry:

The gathering of firms delivering homogeneous item is called industry. Truth be told the idea of industry exists just under flawless challenge. An industry is said to be in harmony when it tends to increment or decline its degree of yield.

As per Prof. Hansen, "An industry will be in harmony when there is no inclination for the size of the business to change i.e., when no organizations wish to leave it and no new firms are being pulled in to it." New firms will tend to enter the business when existing firms are getting a charge out of typical benefits. The ordinary benefits earned by a firm are incorporated into absolute expense.

Along these lines harmony for the business implies that organizations are neither moving in or nor moving out. It implies that the degree of benefits in it is neither above nor underneath the ordinary level and subsequently is equivalent to it.

States of Balance of an Industry:

1. Consistent Number of Firms:

An industry will be in balance when the quantity of firms stays consistent. In this circumstance, no new firms will enter and no old firms will leave the business.

2. Balance of Firms:

An industry will be in balance when all organizations working in it are in balance and tend to increment or decline the degree of yield.

(I) Short Run Balance of Industry:

In the short run, the industry is said to be in Balance when every one of the organizations working under it are in harmony. Be that as it may, for the business to be in full balance in the short run is extremely uncommon. Full balance position is conceivable when firms win typical benefits. In the short run firms can likewise acquire supernormal benefits or cause misfortunes. It tends to be appeared with the assistance of fig. 9.

Short Run Harmony of Industry

In fig. 9 (A) DD is the business' interest bend and SS speaks to the stockpile bend. Both these bends converge each other at