Understanding Gravity Equation, Monopoly, Cournot, and Intra-Industry Trade

Posted on Feb 13, 2025 in Economic Sciences

Gravity Equation

GRAVITY EQUATION:

Τ =????∗????????∗????????/????????

D increases – T decreases / Y increases – T increases

Tij = the value of trade between country i and country j – bilateral trade flow

A = a constant

Yi = GDP of country i (exporter)

Yj = GDP of country j (importer)

Dij = distance between both countries (bilateral trade friction) – impact of distance increased over time (modern transportation over time and communication – hard to find data: Distance puzzle)

Size (GDP): of an economy is directly related to the volume of imports and exports (not quantity); larger economies produce and export more => more income => more money for imports.

Distance: influences transportation costs and therefore costs of imports and exports; can also influence personal contact and communication.

Cultural affinity: cultural ties make economic ties more likely; language is an important barrier to trade.

Geography: ocean harbors and a lack of mountain barriers make transport easier.

Multinational corporations: corporations spread across nations shift their goods between their divisions.

Borders: crossing borders involves formalities and takes time and perhaps tariffs.

log ???????????? = log ???? + ???????????????????????? + ???????????????????????? − ???????????????????????????? + Ɛ????????

  1. The log of bilateral trade flow is explained through the log of a constant and the log of both country’s GDPs reduced by the log of the distance between the countries (plus the error term).
  2. The GDPs have a high positive impact.
  3. The D has an important negative impact.

Findings: Distance should have decreased over time due to globalization. Normally, there should be a “death of distance”. Distance is used as a proxy for transportation costs which declined. Nevertheless, the coefficient “distance” is increasing over time => Distance Puzzle

Monopoly

MONOPOLY:

Many producers in the X sector; perfect competition: pF = MCF / Single producer (monopolist) in the Y sector; profit maximization: pM????(1-1/????) = MCM

At the autarky equilibrium we know:

  1. domestic demand = domestic supply (consump=produc) MRT = MCM/MCF
  2. Utility max. gives: MRS = pM/pF
  3. Profit max. gives: pF = MCF & pM????(1-1/????) = MCM

The autarky equilibrium with a monopoly is not optimal; the equilibrium is distorted:

  1. A higher welfare level can be reached at point pc (= perfect competition, where MRS = MRT = price ratio)
  2. The extent of the distortion (Verzerrung) depends on the ratio MRT / MRS = (1-1/????) and thus on the mark-up of price over marginal cost in the monopoly sector (causing a too low production level of manufactures)

The wedge between MRT and MRS is produced by the mark-up of price from the monopoly. In perfect competition this wedge does not exist anymore (MRT=MRS) because there is no mark-up on price in perfect competition (p=MC).

Cournot

COURNOT:

Demand-price combinations are a function of both outputs, so is each firm’s profit

Firm A maximizes profits given the output level of firm B, say qB0.

Firm A then picks optimal output along line qB0 to max profit, say at point A0 (the higher the quantity, the smaller the price).

To be optimal, firm A’s iso-profit curve must be tangent at point A0.

The curve connecting all firm A’s optimal responses to changes in firm B’s output level is called A’s reaction curve.

If firm B produces a higher level of output, say qB1, firm A will adjust its optimal output.

In this case, it will reduce output to point A1; this point must again be tangent to A’s iso-profit curve.

Similarly for levels qB2, qB3 leading to points A2 and A3.

Obviously, firm A’s profits are maximized if firm B produces nothing as firm A is then a monopolist.

Maximum profits are thus reached at point qmon,A.

Firm A’s iso-profit curves therefore increase in the direction of the arrows towards point qmon,A.

Intra-Industry Trade

INTRA INDUSTRY TRADE:

Is when a country simultaneously imports and exports similar types of goods/services, that is trade within the same industry or sector.

The Dixit-Stiglitz (DS) monopolistic competition model explains intra-industry trade:

  • Paul Krugman realized that the exported goods are usually similar, but not identical to, the imported goods.
  • Consumers like to demand different varieties, Krugman builds on the Dixit-Stiglitz (DS) monopolistic competition model to explain intra-industry trade
  • Utility function: U = utility, i = variety index, ci = consumption of variety i, N = number of varieties, ???? = parameter
  1. The demand for variety i is characterized by constant price elasticity of demand
  2. MR = MC – mark-up – positive operating profits production requires fixed costs fW.
  3. If op > fW firms enter the market, otherwise they exit.
  4. If new firms enter the market, firm i’s demand falls
  5. Output decreases to q’ but, does not affect the price p (constant mark-up)
  6. Operating profits fall.
  7. Firms enter the market until op = fW
  8. Zero-profit condition determines the number of varieties N produced (proportional to the size of the market).