A 2X2X2X2 World

1. 1. Two countries: Westland and Lakeland.
2. 2. Two goods: Westland produces mostly wine and Lakeland produces mostly cheese. P_wn and P_cn denote the price in Westland of wine and cheese in notes currency. P_wp and P_cp denote the price in Lakeland of wine and cheese in pesos currency.
3. 3. Two factors of production: Labor and land.
4. 4. Two currencies: Westland uses notes as its currency and Lakeland uses the peso as its currency.

Equilibrium Under Autarky

The point of intersection of the demand and supply curves (D_L and S_L) is the market “clearing” equilibrium price for cheese, $P_{\text{cp}}^{*}$, and quantity of cheese, $Q_{\text{cl}}^{*}$, produced in Lakeland absent in the international trade.

Similarly, Fig. 1.1B shows the demand (D_w) and supply (S_w) conditions for cheese in the Westland economy. The intersection of the two curves denotes the market clearing price, $P_{\text{cn}}^{*}$, and quantity of cheese produced, $Q_{\text{cw}}^{*}$, in Westland under the autarkic conditions.

Global and National Equilibrium

1. 1. We assume that the economic agents maximize profits.
2. 2. We assume that there are no transaction costs or any frictions restricting the mobility of goods and services across the two economies.

These two assumptions are sufficient to ensure that the profit maximizing agents “arbitrage” any differences in prices across national borders. More than likely the autarky cheese price, the market clearing price that would prevail in the absence of trade will be different in the two localities. In the example depicted in Fig. 1.1, they are, here is how the arbitrage process would work: in the absence of trade between the two countries, $P_{\text{cp}}^{*}$ and $P_{\text{cn}}^{*}$ denote the autarky market clearing price of cheese in Lakeland and in Westland.

$E\times P_{\text{cn}}^{*}>P_{\text{cp}}^{*}$

(1.1)

$\text{Arbitrage profits per unit}=\text{E}\hspace{0.17em}\times \hspace{0.17em}{P}_{\text{cn}}^{*}-P_{\text{cp}}^{*}$

(1.2)

1. 1. After the opening of trade, the higher price per pound of cheese in Westland produce a profit opportunity for the people of Lakeland. In order to take advantage of the higher price in Westland, Lakeland’s producers increase their production in order to export to Westland and take advantage of the higher prices. This is depicted in Fig. 1.2 as an upward movement along Lakeland’s supply curve. The production of cheese will rise from $Q_{\text{cl}}^{*}$ to S_cl.
2. 2. The higher price of cheese in Westland will also affect the Lakeland cheese consumers. As the market price will rise their consumption of cheese will decline. This is depicted in Fig. 1.2 as an upward movement along the demand curve. The local consumption of cheese in Lakeland will fall to Q_cl from $Q_{\text{cl}}^{*}$.
3. 3. The increased production less the reduced consumption in Lakeland leads to a surplus of cheese that is now exported to Westland. Lakeland exports are denoted by X_cl.
4. 4. The lower price for a pound of cheese in Lakeland will produce a profit opportunity for the people of Westland too. In order to take advantage of the lower price, arbitrageurs will import cheese from Lakeland and sell in Westland at a price higher than Lakeland but lower than Westland. The lower price will result in an increase in the quantity demanded of cheese. This is depicted in Fig. 1.2 as a downward movement along Westland’s demand curve for cheese. Westland demand for cheese will increase from $Q_{\text{cw}}^{*}$ to Q_cw. The import competition also puts downward pressure on the price of and production of cheese in Westland. This is depicted in Fig. 1.2 as a downward movement along the supply curve, the production of cheese in Westland will fall to S_cw from $Q_{\text{cw}}^{*}$.
5. 5. Westland cheese imports, M_cw, will be the difference between the domestic consumption of cheese and the domestic production of cheese in Westland, that is, S_cw−Q_cw.

Global equilibrium is depicted in Fig. 1.2 as the intersection of the world demand and supply curve for cheese. The global demand is nothing more than the sum of the two countries demand curves while the global supply is the sum of the two countries supply curves for cheese. The global market clearing prices and quantities of cheese produced can be depicted as $P_{\text{c}}^{\text{e}}$ and $Q_{\text{c}}^{\text{e}}$.

$X_{\text{cl}}=S_{\text{cl}}-Q_{\text{cl}}$

(1.3)

$M_{\text{cw}}=Q_{\text{cw}}-S_{\text{cw}}$

(1.4)

$P_{\text{cp}}=P_{\text{cn}}\times \hspace{0.17em}E$

(1.5)

$P_{\text{wp}}=P_{\text{wn}}\hspace{0.17em}\times \hspace{0.17em}E$

(1.6)

${\text{CPI}}_{\text{p}}={\text{CPI}}_{\text{n}}\times E$

(1.7)

${\pi }_{\text{p}}={\pi }_{\text{n}}+є$

(1.8)

Global Equilibrium and the Trade Accounts

$X_{\text{cl}}=M_{\text{cw}}$

(1.9)

$X_{\text{ww}}=M_{\text{wl}}$

(1.10)

$Y_{\text{i}}=P_{\text{ci}}\hspace{0.17em}\times \hspace{0.17em}{S}_{\text{ci}}+P_{\text{wi}}\hspace{0.17em}\times \hspace{0.17em}{S}_{\text{wi}}$

(1.11)

$C_{\text{i}}=P_{\text{ci}}\hspace{0.17em}\times \hspace{0.17em}{C}_{\text{ci}}+P_{\text{wi}}\hspace{0.17em}\times \hspace{0.17em}{C}_{\text{wi}}$

(1.12)

$\text{T}{\text{B}}_{\text{l}}=P_{\text{wp}}\hspace{0.17em}\times \hspace{0.17em}{M}_{\text{wl}}-P_{\text{cp}}\hspace{0.17em}\times \hspace{0.17em}{X}_{\text{cl}}=0$

(1.13)

$\text{T}{\text{B}}_{\text{w}}=P_{\text{cn}}\hspace{0.17em}\times \hspace{0.17em}{M}_{\text{cw}}-P_{\text{wn}}\hspace{0.17em}\times \hspace{0.17em}{X}_{\text{ww}}=0$

(1.14)

$P_{\text{wp}}\hspace{0.17em}\times \hspace{0.17em}{M}_{\text{wl}}=P_{\text{cp}}\hspace{0.17em}\times \hspace{0.17em}{X}_{\text{cl}}=P_{\text{cn}}\hspace{0.17em}\times \hspace{0.17em}E\hspace{0.17em}\times \hspace{0.17em}{M}_{\text{cw}}=P_{\text{wn}}\hspace{0.17em}\times \hspace{0.17em}E\hspace{0.17em}\times \hspace{0.17em}{X}_{\text{ww}}$

(1.15)

The Terms of Trade or Real Exchange Rate

$\text{T}=P_{\text{wn}}\text{/}{P}_{\text{cn}}=P_{\text{wp}}\text{/}{P}_{\text{cp}}$

(1.16)

Interest Rate Parity

• • If they save 1 peso at home at the end of the year, they receive 1 + i_p, or 1 peso plus the Lakeland/peso interest rate.
• • Alternatively, the investor could have converted the peso into notes at the current spot exchange rate, invested in notes in Westland’s market and earn 1 + i_n at the end of the year, while simultaneously buying a futures contract on the currency that locks in the conversion or exchange rate. Investors would then arbitrage any difference between the two strategies, investing in the home market or foreign market. The end result of the arbitrage is what is called the interest rate parity theorem [7]:

$i_{\text{p}}-i_{\text{n}}=є$

(1.17)

$i_{\text{p}}={\pi }_{\text{p}}+{\rho }_{\text{p}}$

(1.18)

$i_{\text{n}}={\pi }_{\text{n}}+{\rho }_{\text{n}}$

(1.19)

$i_{\text{p}}-i_{\text{n}}={\pi }_{\text{p}}-{\pi }_{\text{n}}+({\rho }_{\text{p}}-{\rho }_{\text{n}})$

(1.20)

${\rho }_{\text{l}}={\rho }_{\text{w}}$

(1.21)

What Happens When the Terms of Trade Change in Predictable Directions?

${\rho }_{\text{l}}={\rho }_{\text{w}}+\tau$

(1.22)

$i_{\text{l}}-i_{\text{w}}=є={\pi }_{\text{l}}-{\pi }_{\text{w}}+({\rho }_{\text{l}}-{\rho }_{\text{w}})$

$i_1-i_{\text{w}}=є={\pi }_1-{\pi }_{\text{w}}+\tau$

$\tau =є-({\pi }_{\text{l}}-{\pi }_{\text{w}})$

(1.23)

Adding the Final X2

$P_{\text{wl}}={\alpha }_{\text{l}}\times W_{\text{wl}}+(1-{\alpha }_{\text{l}})\hspace{0.17em}\times \hspace{0.17em}{R}_{\text{wl}}$

(1.24)

$P_{\text{cl}}={\beta }_{\text{l}}\hspace{0.17em}\times \hspace{0.17em}{W}_{\text{cl}}+(1-{\beta }_{\text{l}})\hspace{0.17em}\times \hspace{0.17em}{R}_{\text{cl}}$

(1.25)

$P_{\text{ww}}={\alpha }_{\text{w}}\times W_{\text{ww}}+(1-{\alpha }_{\text{w}})\hspace{0.17em}\times \hspace{0.17em}{R}_{\text{ww}}$

(1.26)

$P_{\text{cw}}={\beta }_{\text{w}}\times W_{\text{cw}}+(1-{\beta }_{\text{w}})\times R_{\text{cw}}$

(1.27)

$P_{\text{wl}}=E\hspace{0.17em}\times \hspace{0.17em}{P}_{\text{ww}}$

(1.28)

$P_{\text{cl}}=E\hspace{0.17em}\times \hspace{0.17em}{P}_{\text{cw}}$

(1.29)

$W_{\text{wl}}=W_{\text{cl}}$

(1.30)

$W_{\text{ww}}=W_{\text{cw}}$

(1.31)

$R_{\text{wl}}=R_{\text{cl}}$

(1.32)

$R_{\text{ww}}=R_{\text{cw}}$

(1.33)

$P_{\text{wl}}=\alpha \hspace{0.17em}\times \hspace{0.17em}{W}_{\text{l}}+(1-\alpha )\hspace{0.17em}\times \hspace{0.17em}{R}_{\text{l}}$

(1.34)

$P_{\text{cl}}=\beta \hspace{0.17em}\times \hspace{0.17em}{W}_{\text{l}}+(1-\beta )\hspace{0.17em}\times \hspace{0.17em}{R}_{\text{l}}$

(1.35)

$P_{\text{cl}}-P_{\text{wl}}=(\beta -\alpha )\hspace{0.17em}\times \hspace{0.17em}(W_{\text{l}}-R_{\text{l}})$

(1.36)

$W_{\text{l}}-R_{\text{l}}=(P_{\text{cl}}-P_{\text{wl}})/(\beta -\alpha )$

(1.37)

$R_{\text{l}}=(\beta \hspace{0.17em}\times \hspace{0.17em}{P}_{\text{wl}}-\alpha \hspace{0.17em}\times \hspace{0.17em}{P}_{\text{cl}})/(\alpha -\beta )$

(1.38)

$W_{\text{l}\hspace{0.17em}}=\hspace{0.17em}((1-\beta )\hspace{0.17em}\times \hspace{0.17em}{P}_{\text{wl}}\hspace{0.17em}-\hspace{0.17em}(1-\alpha )*P_{\text{cl}})/(\alpha -\beta )$

(1.39)

• • The returns to the cheese intensive factors in the production of cheese in Lakeland rises, while those in Westland declines. If Cheese is the relatively labor intensive factor, then β > α holds at all times and we can safely conclude that in Lakeland, the return to the cheese intensive factor, labor, rises both in absolute terms, Eq. (1.36), as well a rising relative to the Wine intensive factor, see Eq. (1.37). In Westland, the cheese intensive factor experience an absolute and relative decline.
• • The same information also suggests that the returns to the factor intensive in the production of wine rises in absolute and relative terms in Westland while declining in both absolute and relative terms in Lakeland.

$W_{\text{cl}}=W_{\text{wl}}=E\hspace{0.17em}\times \hspace{0.17em}{W}_{\text{cw}}=E\hspace{0.17em}\times \hspace{0.17em}{W}_{\text{ww}}=W$

(1.40)

$R_{\text{cl}}=R_{\text{wl}}=E\hspace{0.17em}\times \hspace{0.17em}{R}_{\text{cw}}=E\hspace{0.17em}\times \hspace{0.17em}{R}_{\text{ww}}=R$

(1.41)

$P_{\text{cl}}=E\hspace{0.17em}\times \hspace{0.17em}{P}_{\text{cw}}$

(1.42)

$P_{\text{wl}}=E\hspace{0.17em}\times \hspace{0.17em}{P}_{\text{ww}}$

(1.43)

• • Free trade in the two finished goods leads to equalizations of the two factor returns even if the factors of production do not move across national borders.
• • Free mobility of the two factors of production leads to equalization of the two factor returns as well as the equalization of the price of the two finished goods even if the finished goods do not move across national borders.

$P_{\text{wl}}=E\hspace{0.17em}\times \hspace{0.17em}{P}_{\text{ww}}$

(1.44)

$W_{\text{cl}}=W_{\text{wl}}=E\hspace{0.17em}\times \hspace{0.17em}{W}_{\text{cw}}=E\hspace{0.17em}\times \hspace{0.17em}{W}_{\text{ww}}=W$

(1.45)

$R_{\text{c1}}=R_{\text{wl}}$

(1.46)

$E\hspace{0.17em}\times \hspace{0.17em}{R}_{\text{cw}}=E\hspace{0.17em}\times \hspace{0.17em}{R}_{\text{ww}}$

(1.47)

$P_{\text{wl}}=E\hspace{0.17em}\times \hspace{0.17em}{P}_{\text{ww}}$

$\alpha \hspace{0.17em}\times \hspace{0.17em}W+(1-\alpha )\hspace{0.17em}\times \hspace{0.17em}{R}_{\text{wl}}=\alpha *W+(1-\alpha )\times \hspace{0.17em}{R}_{\text{ww}}\hspace{0.17em}\times \hspace{0.17em}E$

(1.48)

$R_{\text{wl}}=R_{\text{ww}}\hspace{0.17em}\times \hspace{0.17em}E$

(1.49)

$R_{\text{cl}}=R_{\text{wl}}=E\hspace{0.17em}\times \hspace{0.17em}{R}_{\text{cw}}=E\times R_{\text{ww}}=R$

(1.50)

Mobility, Trade, and the Equalization of Price and Factor Returns Across Borders

Transportation Costs and Overall Equilibrium

• • The wedge or difference between the price paid by the importers in pesos, $P_{\text{cn}}^{\text{t}}$*E and the price received by the exporters, $P_{\text{cp}}^{\text{t}}$, is nothing more than the transportation costs, TC. In equation form, the wedge or price difference can be written as: TC = $P_{\text{cn}}^{\text{t}}$*E−$P_{\text{cp}}^{\text{t}}$
• • The global quantity demanded consumed, $Q_{\text{c}}^{\text{t}}$, will match the global quantity supplied or produced, $Q_{\text{c}}^{\text{t}}$.

• • The transportation costs for the export of cheese account for 10% of the price of a pound of cheese in Westland.
• • The transportation costs for the import of a bottle of wine account for 25% of the price of a bottle of wine in Lakeland.
• • The ratio of the price of a pound of cheese and a bottle of wine show that in Lakeland it takes 100 bottles of wine to get 200 pounds of cheese.
• • However, in Westland it takes 100 bottles of wine to acquire 136 pounds of cheese.

• • The rate of exchange in the two localities shows that cheese is relatively more expensive in Westland than in Lakeland.
• • The direct arbitrage opportunities have been exhausted; the peso prices of a pound of cheese and a bottle of wine in the two economies differ by exactly the transportation costs.

• • 100 bottles of wine in Westland fetches 136 pounds of cheese.
• • 100 bottles of Westland wine will fetch 200 pounds of cheese in Lakeland.
• • There therefore is a potential arbitrage gain of 74 pounds of cheese.

Mobility and the Incidence of Taxes and Other Economic Shocks

$P_{\text{c}}^{*}\hspace{0.17em}\times (1-\text{t})$

where $P_{\text{c}}^{*}$ is the worldwide equilibrium price for cheese and t is the export tax rate. A 10% tax in a product is equivalent to a tax on each for the factors of production. Labor is assumed to be free to move across national borders, this means that labor or any other mobile factor has to earn the same after tax rate of return as anywhere else in the world, $W_{\text{e}}^{*}$, otherwise it will leave the country in search of the higher rate of return. Therefore the salaries paid in Lakeland to the mobile factor have to be grossed by the tax.

$P_{\text{c}}^{*}\hspace{0.17em}\times \hspace{0.17em}(1-\text{t})=[\beta *W_{\text{l}}+(1-\text{b})\hspace{0.17em}\times \hspace{0.17em}R/(1-\text{t})]\hspace{0.17em}\times \hspace{0.17em}(1-\text{t})$

(1.51)

$\begin{array}{l}{W}_{\text{l}}=[P_{\text{c}}^{*}\hspace{0.17em}\times \hspace{0.17em}(\text{1}-\text{t})-(\text{1}-\text{b})\hspace{0.17em}\times \hspace{0.17em}R]/[\text{b}\hspace{0.17em}\times \hspace{0.17em}(\text{1}-\text{t})]\\ =(P_{\text{c}}^{*}/\text{b})+\{(\text{1}-\text{b})\hspace{0.17em}\times \hspace{0.17em}R/[\text{b}*(\text{1}-\text{t})]\}\end{array}$

(1.52)

Since $P_{\text{c}}^{*}$ and W are determined in the world economy and we have assumed that the small economy, Lakeland, has no global market power. The only variable Lakeland can affect is the export tax rate. The previous equation shows that the increases in the tax rate lower the equilibrium wage rate. The incidence of the tax rate increase depends in the intensity of the immobile factor in the production of cheese. The lower the intensity of the immobile factor the greater the impact of the tax rate on the equilibrium rate of return of the immobile factor.

The Speed of Adjustment to a New Equilibrium