A new building to be located in a cold climate is being designed with a basement that has an L 200-mm-thick wall. Inner and outer basement wall temperatures are Ti 20 C and To 0 C, respectively. The architect can specify the wall material to be either aerated concrete block with kac 0.15 W/mK, or stone mix concrete. To reduce the conduction heat flux through the stone mix wall to a level equivalent to that of the aerated concrete wall, what thickness of extruded polystyrene sheet must be applied onto the inner surface of the stone mix con crete wall? Floor dimensions of the basement are 20 m 30 m, and the expected rental rate is $50/m2 / month. What is the yearly cost, in terms of lost rental income, if the stone mix concrete wall with polystyrene insulation is specified?
Econ 202 ~ Chapter 6 ~ Measuring the Cost of Living How the CPI is calculated The consumer price index shows the “cost” of a basket of goods and services “relative to the cost” of the same basket in the base year. The index is used to measure the “overall level of prices” in the economy. The percentage change in the consumer price index measures the inflation rate. CPI measures the overall cost of the goods and services purchased by a typical household. The CPI measures the typical cost of living, inflation and the inflation rate. Inflation rate ~ is the percentage of change in the “current” CPI from a previous CPI CPI = Price of basket of G&S in current year / Price of basket in base year X 100 Inflation rate = CPI (t) – CPI (t-1) / CPI (t-1) X 100 The goal of the CPI is to measure the changes in costs of living How this is done: 1. Fix the basket 2. Find the prices 3. Compute the basket’s cost (this isolates price changes from any quantity changes) 4. Choose a base year and compute the index 5. Compute the inflation rate The BLS (Bureau of Labor and Statistics) calculates several other price indexes. The BLS computes indexes for certain areas; such as, Boston, New York and Los Angeles. The BLS also tracks narrow categories; such as, food, clothing and energy. The BLS (Bureau of Labor and Statistics) also calculates the PPI (Producer Price Index). The PPI measures the “cost” of a basket of goods and services purchased by firms rather than by the consumers. Changes in the PPI are thought to be useful in predicting changes in the CPI. Problems in Measuring the Cost of Living The consumer price index is an imperfect measure of the cost of living for three reasons. (1) First, it does not take into account consumers’ ability to substitute toward goods that become relatively cheaper over time. (2) Second, it does not take into account increases in the purchasing power of the dollar due to the introduction of new goods. (3) Third, it is distorted by unmeasured changes in the quality of goods and services. Because of these measurement problems, the CPI overstates true inflation and increases in cost of living: This can be seen in COLA (cost of living adjustment) by 0.5%. This effects social security too. Substitution Bias ~ CPI overstates increases in costs of living because of cheaper items used in order to replace higher priced items New Goods ~ CPI doesn’t reflect increased purchasing power of the dollar due to more variety ~ the dollar increases in value Quality Changes ~ CPI doesn’t reflect product improvements and increased dollar value ~ this occurs if prices remain the same when quality improves The GDP Deflator versus the Consumer Price Index (CPI) Like the consumer price index, the GDP deflator (dGDP) measures the overall level of prices in the economy. The two price indexes “usually” move together, but there are important differences: (1) The GDP deflator differs from the CPI because it (dGDP) includes goods and services produced rather than goods and services consumed. As a result, imported goods affect the consumer price index but not the GDP deflator. (2) In addition, while the consumer price index uses a fixed basket of goods, the GDP deflator automatically changes the group of goods and services over time as the composition of GDP changes. (3) The dGDP excludes consumer goods that are imported; whereas, the CPI includes imported consumer goods. (4) The dGDP (GDP deflator) includes capital goods; whereas, the CPI excludes capital goods because of its consumer orientation. The Matrix: PRODUCED DOMESTICALLY YES NO CONSUMER YES CPI & dGDP CPI GOODS NO dGDP null GDP Deflator (dGDP) CPI Excludes imported consumer goods Includes Imported consumer goods Includes capital (hard assets) goods Excludes capital goods Basket of goods change with time Uses (fixed) unchanged basket of goods Measures what is produced Measures only what’s purchased/consumed Measures inflation rate by percentage Measures inflation rate by percentage changes from prior periods changes from prior periods Measures overall prices Measures overall prices Dollar Figures from Different Times Dollar figures from different times do not represent a valid comparison of purchasing power. To compare a dollar figure from the past to a dollar figure today, the older figure should be inflated using a price index. Calculations of a dollar’s purchasing power Amount in today’s dollars = Yesteryear’s Dollar X CPI Today/CPI of Yesteryear Indexation Various laws and private contracts use price indexes to correct for the effects of inflation. The tax laws, however, are only partially indexed for inflation. Indexation ~ is the automatic correction by law or contract of a dollar amount for the effects of inflation. Used in the cost-of-living-allowance (COLA) and social security calculations Inflation makes it harder to compare dollar amounts from different times. Comparing Dollar Figures from Different times This technique to convert a time series of current-dollar (nominal) figures into constant-dollar (real) figures: CPI today / CPI yesteryear (increase in overall cost of living per time) Shows how a variable has changed over time after correcting for inflation Shows what happens to one’s purchasing power Real and Nominal Interest Rates A correction for inflation is especially important when looking at data on interest rates. The nominal (current, recent) interest rate is the interest rate usually reported; it is the rate at which the number of dollars in a savings account increase over time. By contrast, the “real interest rate” takes into account changes in the value of the dollar over time. The real interest rate equals the nominal (current, recent) interest rate minus the rate of inflation. Real interest rate = Nominal interest rate – Inflation rate Inflation rate = Nominal interest rate – Real interest rate (It’s the “gap” between lines) Nominal interest rate ~ is the interest rate as usually reported without a correction for the effects of inflation in dollar value Real interest rate ~ is the rate corrected for the effects of inflation in regards to growth or loss in the purchasing power of a deposit or debt