From Oatley 2014 p214++
Balance-of-Payments Adjustment
Even though the current and capital accounts must balance each other, there is no assurancethat the millions of international transactions that individu- als, businesses, and governments conduct every year will necessarily produce this balance. When they don’t, the country faces an imbalance of payments. A country might have a current-accountdeficit that it cannotfully finance throughcapital imports, for example, or it might have a current-accountsur- plus thatis not fully offset by capital outflows. When an imbalancearises, the country must bring its payments back into balance. The process by which a country doessois called balance-of-payments adjustment. Fixed and floating exchange-rate systems adjust imbalances indifferent ways.
In a fixed exchange-rate system, balance-of-payments adjustment occurs through changes in domestic prices. We can most readily understand this ad- justmentprocess through a simple example. Suppose there are only two coun- tries in the world—the United States and Japan—and supposefurther that they maintain a fixed exchange rate according to which $1 equals 100 yen. The United States has purchased 800 billion yen worth of goods, services, and financial assets from Japan, and Japanhas purchased $4 billion of items from the United States. Thus, the United States has a deficit, and Japan a surplus, of $4billion.
This payments imbalance creates an imbalance between the supply of and the demandfor the dollar and yen in the foreign exchange market. American residents need 800 billion yen to pay for their imports from Japan. They can acquirethis 800 billion yen by selling $8 billion. Japanese residents need only $4 billion to pay for their imports from the United States. They can acquire the $4 billion by selling 400billion yen. Thus, Americanresidentsareselling $4 billion more than Japanese residents want to buy, and the dollar depreci- ates againstthe yen.
Because the exchangerateis fixed, the United States and Japan must prevent this depreciation. Thus, both governmentsintervenein the foreign exchange market, buying dollars in exchange for yen. Intervention has two consequences.First, it eliminates the imbalance in the foreign exchange mar- ket as the governments provide the 400billion yen that American residents need in exchange forthe $4 billion that Japanese residents do not want. With the supply of each currency equalto the demandin the foreign exchange mar- ket, the fixed exchangerate is sustained. Second, intervention changes each country’s money supply. The American moneysupply falls by $4 billion, and Japan’s moneysupplyincreases by 400billion yen.
The change in the money supplies alters prices in both countries. The reduc- tion of the U.S. money supply causes Americanpricesto fall. The expansion of the money supply in Japan causes Japanese prices to rise. As American prices fall and Japanese prices rise, American goods becomerelatively less expensive than Japanese goods. Consequently, American and Japaneseresidents shift their purchases away from Japanese products and toward American goods. American imports (and hence Japanese exports) fall, and American exports (and hence Japanese imports) rise. As American imports (and Japanese exports) fall and American exports (and Japanese imports) rise, the payments imbalanceis elimi- nated. Adjustment underfixed exchange rates thus occurs through changesin the relative price of American and Japanese goods brought about by the changes in moneysupplies caused by intervention in the foreign exchange market.
In floating exchange-rate systems, balance-of-payments adjustment oc- curs through exchange-rate movements. Let’s go back to our U.S.—Japan sce- nario, keeping everything the same, exceptthis time allowing the currencies to float rather than requiring the governments to maintain a fixed exchangerate. Again,the $4 billion payments imbalance generates an imbalancein the for- eign exchange market: Americansare selling more dollars than Japanese resi- dents want to buy. Consequently, the dollar begins to depreciate against the yen. Because the currencies are floating, however, neither governmentinter- venesin the foreign exchange market. Instead, the dollar depreciates until the marketclears. In essence, as Americans seek the yen they need, they are forced to accept fewer yen for each dollar. Eventually, however, they will acquire all of the yen they need, but will have paid more than $4 billion for them.
The dollar’s depreciation lowers the price in yen of American goods and services in the Japanese market andraises the price in dollars of Japanese goodsandservices in the American market. A 10 percent devaluation of the dollar against the yen, for example, reduces the price that Japanese residents pay for American goods by 10 percentandraises the price that Americans pay for Japanese goods by 10 percent. By making American products cheaper and Japanese goods more expensive, depreciation causes American imports from Japan to fall and American exports to Japan to rise. As American exports expand and importsfall, the payments imbalanceis corrected.
In both systems, therefore, a balance-of-payments adjustment occurs as prices fall in the country with the deficit and rise in the country with the surplus. Consumers in both countries respond to these price changes by purchasing fewer of the now-more-expensive goods in the country with the surplus and more of the now-cheaper goodsin the country with the deficit. These shifts in consumption alter imports and exports in both countries, mov- ing each of their payments back into balance. The mechanism that causes these price changes is different in each system, however. In fixed exchange- rate systems, the exchange rate remains stable and price changes are achieved by changing the moneysupplyin orderto alter prices inside the country. In floating exchange-rate systems, internal prices remain stable, while the change in relative prices is brought about through exchange-rate movements.
Contrasting the balance of payments adjustment process under fixed and floating exchangerates highlights the trade off that governments face between
exchangerate stability and domestic price stability: Governments can have a stable fixed exchangerate or they can stabilize domestic prices, but they cannotachieve both goals simultaneously. If a government wants to maintain a fixed exchangerate, it must accept the occasional deflation and inflation caused by balance-of-payments adjustment. If a governmentis unwilling to accept such price movements,it cannot maintain a fixed exchangerate. This trade-off has been the central factor driving the international monetary system toward floating exchange rates during the last 100 years. We turn now to examine howthis trade-off first led governmentsto create innovativeinter- national monetary arrangements following World WarII and then caused the system to collapse into a floating exchange-rate system in the early 1970s.
The Logistic Map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. The map was popularized in a seminal 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation first created by Pierre François Verhulst.
Mathematically, the logistic map is writtenwhere:
is a number between zero and one, and represents the ratio of existing population to the maximum possible population at year n, and hence x0 represents the initial ratio of population to max. population (at year 0)r is a positive number, and represents a combined rate for reproduction and starvation.For approximate Continuous Behavior set 'R Base' to a small number like 0.125To generate a bifurcation diagram, set 'r base' to 2 and 'r ramp' to 1
To demonstrate sensitivity to initial conditions, try two runs with 'r base' set to 3 and 'Initial X' of 0.5 and 0.501, then look at first ~20 time steps
Model description:
This model is designed to simulate the Covid-19 outbreak in Burnie, Tasmania by estimating several factors such as exposed population, infection rate, testing rate, recovery rate, death rate and immunity loss. The model also simulates the measures implemented by the government which will impact on the local infection and economy.
Assumption:
Government policies will reduce the mobility of the population as well as the infection. In addition, economic activities in the tourism and hospitality industry will suffer negative influences from the government measures. However, essential businesses like supermarkets will benefit from the health policies on the contrary.
Variables:
Infection rate, recovery rate, death rate, testing rate are the variables to the cases of Covid-19. On the other hand, the number of cases is also a variable to the government policies, which directly influences the number of exposed.
The GDP is dependent on the variables of economic activities. Nonetheless, the government’s lockdown measure has also become the variable to the economic activities.
Interesting insights:
Government policies are effective to curb infection by reducing the number of exposed when the case number is greater than 10. The economy becomes stagnant when the case spikes up but it climbs up again when the number of cases is under control.
Overview:
The COVID-19 Outbreak in Burnie Tasmania shows the process of COVID-19 outbreak, the impacts of government policy on both the COVID-19 outbreak and the GDP growth in Burnie.
Assumptions:
We set some variables at fix rates, including the immunity loss rate, recovery rate, death rate, infection rate and case impact rate, as they usually depend on the individual health conditions and social activities.
It should be noticed that we set the rate of recovery, which is 0.7, is higher than that of immunity loss rate, which is 0.5, so, the number of susceptible could be reduced over time.
Adjustments: (please compare the numbers at week 52)
Step 1: Set all the variables at minimum values and simulate
results: Number of Infected – 135; Recovered – 218; Cases – 597; Death – 18,175; GDP – 10,879.
Step 2: Increase the variables of Health Policy, Quarantine, and Travel Restriction to 0.03, others keep the same as step 1, and simulate
results: Number of Infected – 166 (up); Recovered – 249 (up); Cases – 554 (down); Death – 18,077 (down); GDP – 824 (down).
So, the increase of health policy, quarantine and travel restriction will help increase recovery, decrease confirmed cases, decrease death, but also decrease GDP.
Step 3: Increase the variables of Testing Rate to 0.4, others keep the same as step 2, and simulate
results: Number of Infected – 152 (down); Recovered – 243 (down); Cases – 1022 (up); Death – 17,625 (down); GDP – 824 (same).
So, the increase of testing rate will help to increase the confirmed cases.
Step 4: Change GDP Growth Rate to 0.14, Tourism Growth Rate to 0.02, others keep the same as step 3, and simulate
results: Number of Infected – 152 (same); Recovered – 243 (same); Cases – 1022 (same); Death – 17,625 (same); GDP – 6,632 (up).
So, the increase of GDP growth rate and tourism growth rate will helps to improve the GDP in Burnie.
Economic capital growth in a system constrained by a non-renewable resource, Figure 37 from Thinking in Systems by Donella H. Meadows
