ECON 222, Spring 2009 Assignment #1, Answer Key

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1 ECON 222, Spring 2009 Assignment #, Answer Key Question (30 marks) a) This question asks to nd the contributions of the transactions to 2009 s GDP. ou must explain your reasoning behind each of the contributions to obtain full marks for this question. Product approach $00: BikeCo s output valued at $200 ($25 for the mountain bike sold to Tommy and $75 for the unsold bike in inventory) + inventory investment of (-$00) (material purchased from MaterialCo in 2008).Note that the old track bike was not produced in 2009 and should not be included in GDP. Expenditure approach $00: $25 for the mountain bike purchased by Tommy + (-$25) as changes in inventories ($75 for the unsold mountain bike + (-$00) for the materials purchased in 2008). Income approach $00: $50 BikeCo s pro ts + $40 workers wage + $0 government taxes. b) i) Ex post Fisher Equation: i t r EP;t + t Ex post real interest rate (for period t) r EP;t i t - t Where i t Nominal interest rate (for period t) t In ation rate (realised during period t) Period ex post real interest rate i % Period 2 ex post real interest rate i % Period 3 ex post real interest rate i % ii) Ex ante Fisher Equation: i t r EA;t + e t Ex ante real interest rate (at time t) r EA;t i t - e t Where: Expected in ation rate (for period t) e t t Here: e 2 % and e 3 2 2% So, Period 2 ex ante real interest rate i 2 - e 2 5-4% Period 3 ex ante real interest rate i 3 - e % iii) Unpleasantly surprised as they receive a real return (ex post) of 3% but when they made the loan they expected a real return (ex ante) of 4% (get a lower real return then they expected). (Makes a loan means they are lending money! If they were borrowing we would say takes out a loan, borrows or something like that.)

2 Question 2 (35 marks) a) i) Nominal GDP is the total value of goods and services measured at current prices. So, Nominal GDP 2000 (Pcars 2000 Q 2000 cars) + (P 2000 ($0 500; 000) $0; 000; 000 Nominal GDP 2020 (Pcars 2020 Q 2020 cars) + (P 2020 ($20 400; 000) $5; 200; 000 milk Q2000 milk milk Q2020 milk ) ($50; ) + ) ($60; ) + ii) Real GDP is the total value of goods and services measured at constant prices. Therefore, to calculate real GDP in 2020 (base year 2000), multiply the quantites purchased in the year 2020 by the 2000 prices: Real GDP 2020 (Pcars 2000 Q 2020 cars) + (P ; 000) $0; 000; 000 milk Q2020 milk ) ($50; ) + ($0 Real GDP for 2000 is calculated by multiplying the quantities in 2000 by the prices in Since the base year is 2000, real GDP 2000 equals nominal GDP 2000, which is $0, 000, 000. Hence real GDP stayed the same between 2000 and iii) The implicit price de ator for GDP compares the current prices of all goods and services produced to the prices of the same goods and services in a base year. It is calculated as follows: GDP De ator 2020 Nominal GDP2020 Real GDP 2020 $5,200,000 $0,000,000 :52 This calculation reveals that prices of the goods produced in the year 2020 increased by 52 percent compared to the prices that the goods in the economy sold for in (Because 2000 is the base year, the value for the implicit price de ator for the year 2000 is.0 because nominal and real GDP are the same for the base year). iv) The consumer price index (CPI) measures the level of prices in the economy. The CPI is called the xed-weight index because it uses a xed basket of goods over time to weight prices. If the base year is 2000, the CPI in 2020 is an average of prices in 2020, but weighted by the composition of the goods produced in The CPI 2020 is calculated as follows: CPI 2020 : (Pcars Q cars )+(Pmilk Q2000 milk ) (Pcars 2000Q2000 cars )+(P 2000 milk Q2000 milk ) ($60;00000)+($20500;000) ($50;00000)+($0500;000) $6;000;000 $0;000;000 This calculation shows that the price of the goods purchased in 2020 increased by 60 percent compared to the prices these goods would have sold for in The CPI for 2000, the base year, equals.0. 2

3 b) The GDP de ator is Paasche index because it is computed with a change basket of goods; the CPI is a Laspeyres index because it is computed with a xed basket of goods. From part a) the GDP de ator for 2020 is.52, which indicates that prices rose by 52 percent from what they were in The CPI for the year 2020 is.6 which indicates that prices rose by 60 percent from what they were in If prices of all goods rose by 50 percent, for example, then we could say unambiguously that the price level rose by 50 percent. et, in this case, relative prices have changed. The price of cars rose by 20 percent and the price of milk rose by 00 percent, making milk relatively more expensive. As the discrepancy between the CPI and the GDP de ator illustrates, the change in the price level depends on how the goods prices are weighted. The CPI weights the price of goods by the quantities purchased in the year The GDP de ator weights the price of goods by the quantities purchased in The quantity of milk consumed was higher in 2000 than 2020, the CPI places a higher weight on milk. Since the price of milk increased relatively more than the price of cars, the CPI shows a larger increase in the price level. c) There is no obvious answer to this question. Ideally, one wants a measure of the price level that accurately captures the cost of living. As a good becomes relatively more expensive, people buy less of it and more of the other goods. In this case, consumers bought less milk and more cars. An index with xed weights, such as CPI, overestimates the change in the cost of living because it does not take into account that people can substitute less expensive goods for the ones that become more expensive. On the other hand, an index with changing weights, such as the GDP de ator, underestimates the change in the cost of living because it does not take into account that these induced substitutions make people less well o. Question 3 (35 Marks) a) The expressions for the marginal productivities are as follows: MP K K N L MP N K N L MP L b) i) As we can see from the gure below, the marginal productivity of labour is decreasing, but the rate at which it decreases diminishes with N. That is, the MP N is a convex function. 3

4 MPN ii) When the wage paid to labour is p N 2 the level of employment in the economy is N 9. To get this result we need to impose that the labor market is in equilibrium, that is that the price of labor is equal to its marginal product: p N MP N (N)! 2 K N L 2 3N 2! N 2 3! N 9 p 9N 2 p iii) We need to see the behaviour of the derivative of the MPN N (K; N; This quantity is negative, since > 0; ( get decreasing marginal product of labor. ( ) K N 2 L ( ) K L N 2 ) < 0;and K L N 2 > 0. Again, we iv) The table reports the values requested. Notice that each input is essential to production, that is if we do not use any labor we don t get any output no matter what the capital stock is. The same comment applies for capital (and 4

5 land). Production is increasing monotonically in the quantity of inputs. But, since in our example the curvature is more pronounced in K (that is > ), if we compare the change in output deriving from a change in one of the inputs (keeping the other xed) this is higher for capital. In other words, if we compare the marginal product of capital and the marginal product of labor, for the same pairs of values of K and N (with inverted roles in the two marginal products), the MP K is always higher than the MP N. K0 K K2 K4 K6 N N 0 :62 2:64 6:96 N2 0 :23 2 3:25 8:57 N4 0 :52 2:46 4 0:56 N6 0 2:30 3:73 6:06 6 c) i) The expressions for the factors incomes are as follows: p K K MP K K K N L K p N N MP N N K N L K p L L MP L L K ii) If they are between 0 and,,, and always represent the income share of the factor they are the exponent of: For capital p KK For labor p N N For land p LL iii) We need to impose that + +, that is that the production function shows constant returns to scale. To see this, we need to impose the condition that the sum of factor payments is equal to output: p K K + p N N + p L L Substituting in the left hand side the expressions we obtained in point a) gets: + + ( + + ) ( + + ) It follows that if + + : ( + + ) 5