Question

Suppose Tokyo is planning to construct a new public park. Based on some market research, they have determined that the town’s 50 residents can be divided into two types with respect to their benefit from this public good. 20 of the town’s residents are of Type 1 and the other 30 residents are of Type 2. Each resident's individual demand for acres of park space is given by:

Type 1: Q_D = 20 – P

Type 2: Q_D = 40 – 2P

a. Solve for the aggregate demand of Tokyo’s 50 residents as a function of the number of acres. Be sure to write down equations for each section of the aggregate demand curve, as well as the interval of quantities each section spans.

b. Graph the aggregate demand curve calculated in part a. Make sure to label both intercepts, slopes, and the intersection of the two sections.

c. Suppose each acre of public park has a marginal cost of MC = 200 + Q . Solve for the socially efficient number of acres for the town to construct.

d. Calculate the total surplus the 50 residents of Tokyo's gain from constructing this public park.

Answer 1

a)

• Aggregate demand is the demand for all goods and services in an economy.
• The law of demand says people will buy more when prices fall.
• The demand curve measures the quantity demanded at each price.
• The five components of aggregate demand are consumer spending, business spending, government spending, and exports minus imports.
• The aggregate demand formula is AD = C + I + G +(X-M).

• The aggregate demand curve shows the quantity demanded at each price. It's used to show how a country's demand changes in response to all prices. It's similar to the demand curve used in microeconomics. That shows how the quantity of one good or service changes in response to price. The relationship between price and demand is illustrated in the aggregate demand curve below.

The aggregate demand curve says that real GDP will decline when price rises.

Five Components of Aggregate Demand

There are five components of aggregate demand. Everything purchased in a country is the same thing as everything produced in a country. As a result, aggregate demand equals the gross domestic product of that economy.These are the same as the components of GDP.

1. Consumer spending. That's what families spend on final products that aren't used for investment.
2. Investment spending by business. It only includes purchases of equipment, buildings, and inventory.
3. Government spending on goods and services. It does not include transfer payments, such as Social Security, Medicare, and Medicaid. They aren't included because they don't increase demand. These programs shift demand from one group (taxpayers) to another (beneficiaries).
4. Exports. That's demand from other countries.
5. Minus imports. They are demands made by U.S. residents that can't be met by domestic production. So, the demand leaves the economic system of the United States.

Aggregate Demand Formula

Aggregate demand is measured by the following mathematical formula.

AD = C + I + G +(X-M)

It describes the relationship between demand and its five components.

Aggregate Demand = Consumer Spending + Investment Spending + Government Spending + (Exports-Imports)

b)