Econ 222B F2000
Mid-Term Questions and Solutions:
Part I:1. The country of Old Jersey produces milk and butter, and it has published the following macroeconomic data, where quantities are in gallongs and prices are in dollars per gallon.
1998 1999
Good Quantity Price Quantity Price
Milk 500 $2 900 $3
Butter 2000 $1 3000 $2
(i) Calculate the percentage change in the price level between 1998 and 1999 as measured by a variable-weight price index.
Answer:
Variable Weight Price Index:Base, 1998 = 100 (no need for calculation)
Index 1999 = 100 x (1999 Quantities x 1999 Prices) / (1999 Quantities x 1998 Prices)
= 100 x ((900 x 3) + (3000 x 2)) / ((900 x 2) + ((3000 x 1))
=181.25The percentage change in price level is: PoI1999 - PoI1998 = 181.25-100 = 81.25%
{it is still correct if you use Base Index = 1 but in that case you need to multiply by 100 to get the percentage.} (ii) Calculate the real GDP in 1999 using the price index calculated in part (i).
Answer:
Real GDP in 1999= 100 x (Nominal GDP 1999)/(Price Index 1999) = 100 x (1999 Quantities x 1999 Prices)/181.25 = 100 x (8700/181.25) =4800 2. Monica grows coconuts and catches fish. Last year she harvested 1500 coconuts and 600 fish. She values on fish as worth 3 coconuts. She gave Rachel 300 coconuts and 100 fish for helping her harvest coconuts and catch fish, all of which was consumed by Rachel. Monica set aside 200 fish to help with next year's harvest. Use the income approach to calculate the GDP in this island economy in terms of fish. Explain your steps.Answer:
GDP(Income)= Income of Monica + Income of Rachel Monica's Income = (1500-300)Coconuts + (600-100)Fish Rachel's Income = 300 Coconuts + 100 Fish -------------------------------------- GDP = 1500 Coconuts + 600 Fish = 500 Fish + 600 Fish = 1100 Fish3. Derive the expression for the Uses-Of-Savings identity, starting from the definition of private disposable income. Explain its meaning using an example. If a government in an open economy incurs a budget deficit, what are the possibilities of financing it according to the uses-of savings identity? Answer:
Private disposable income = PI PI = GNP - Taxes + Transfers + Interest = Y + NFP - T + TR + INT Private Savings = Spvt = PI - Consumption Spvt = Y + NFP - T + TR + INT - C = C + I + G + NX + NFP - T + TR +INT -C = I +[G-T+TR+INT] + [NX+NFP] = investment + gov't deficit + current acct. Spvt = I + (-Sgvt) + CA Private savings can be used for financing private investment, financing gov't deficit or CA surplus (lending to foreiners). =>Gov't deficit can be financed by private savings or by running down current account (CA<0) =>borrowing from abroad.4. Explain the similarities and differences between the following two: Consumer price index and GDP deflator Answer:
Similarities: -CPI and GDP deflator both measure price level in the economy Differences: -CPI is based on fixed weight index -GDP deflator is a variable weight index CPI, therefore, measures the change in the price of buying a fixed(expenditures of a representative Canadian household) bundle of goods, whereas the GDP deflator measures the average price level of all final goods produced in the economy.
5. Explain whether each of the following statements is true, false or uncertain: (be brief) a) If a Canadian construction company built a road in Kuwait, this activity would be included in Kuwait's GDP. b) Suppose Toyota built a new automobile plant in Mexico using Japanese management practices and Mexican labour. The portion of output contributed by Mexican labour would be included in Mexican GDP but not in Mexican GNP. c) Private disposable income equals NNP+NFP-Taxes+Transfers+Interest. d) Because government services are not sold in markets, the government tries to estimate their market value and uses this to measure the government's contribution to GDP. e) If the price index last year was 1.0 and today it is 1.4, the inflation rate over this period is 1.4% Answer:
a) True: the activity takes place in Kuwait so it will be included in their GDP. b) False: It will be included in both measures. c) False: PDI = GNP - taxes + transfers + interest d) False: government services are valued at the cost of provision. e) False: inflation rate = 1.4-1.0 = 40% not 1.4%6. For the economy of Lower Volta, the MPN (marginal product of labour) is given by: MPN = 400-0.5N, where N is the aggregate employment. The aggregate quantity of labour supplied is: N = 500+w. Calculate the level of aggregate employment and real wage in equilibrium. Answer:
dd F'n: w = MPN = 400-0.5N (1) ss F'n: N = 500 + w Solving: substitute (2) into (1) N = 500 + [400 - 0.5N] => 1.5N=900 => N=600 =>w=400-0.5(600) =100
7. Explain what is meant by full employment output. Explain how the full-employment output will be affected by an economy wide beneficial productivity shock. Draw diagrams and explain. Answer:
Part II 1. You are given the following behavioral relationships for the economy of Onga. Labour Market: Marginal Product of Labour = MPN = 500 - 0.5N , N=aggregate employment Labour supply = N = 500 + 0.5w , w=real wage rate Goods Market: Consumption Function = Cd = 200 + 0.9Y - 10000r , r=real interest rate Investment Function = Id = 1000 - 10000r Government = G = 300 a) Calculate the equilibrium real wage (w) and aggregate employment (N) b) Assuming that full-employment output is 5000, derive the desired savings function. c) Explain the goods market equilibrium condition. Solve the equilibrium value of r (assuming full-employment output is 5000). Also, calculate the level of desired consumption and desired savings in equilibrium. d) Suppose that there is a temporary increase in gov't spending financed by borrowing in the market. Explain how it will affect the goods market equilibrium, and the equilibrium levels of real interest rate, desired savings and desired consumption. Draw a diagram to illustrate the changes in the goods market equilibrium. Answer:
a) w= 500 - 0.5N N= 500 + 0.5w => N*=600 and w*=200 b) Yf=Y=5000 Sd= Y - Cd - G = Y - (200 +.9Y -10000r) - 300 = 0.1Y - 500 + 10000r =0.1(5000) -500 + 10000r =500-500+10000r =10000r as r increases Sd increases =>positively sloped function c) Goods Market equilibrium condition: Sd=Id or Y=Cd+Id+G using the first => 10000r=1000-10000r 20000r=1000 r=1000/20000 =0.5 or 5% so: Cd= 200 + 0.9(5000) - 10000r = 200 + 4500 - 500 = 4200 Sd= 10000(0.05) = 500 Id= 500 => Cd+Id+G = 4200+500+300=5000 = Yf d)
2. This question consists of two parts: a) A firm has a current and future marginal productivity of capital given by: MPK = 5000 - 2K The price of capital is $1000. The real interest rate is 10% and the depreciation rate is 10%. Calculate the tax rate on firm's revenue(/&tau) if the desired capital stock(K) is equal to 150. Calculate the tax-adjusted user cost of capital. (note: some bowsers don't support the code used here for the lower case greek letter tau. If you see the symbol /&tau it should be the lower case greek letter tau.) b) Explain how each of the following events will affect the equilibrium real interest rate and equilibrium desired savings. Depict the change in the goods market equilibrium in a diagram (for each case). (i) A technological improvemnt that increase the expected future marginal product of capital. (ii) A temporary increase in income taxes with current and future government spending unchanged, assuming Ricardian Equivalence. (iii) A stock market crash. Answer:
a) MPK = 5000 - 2K K = 150 => MPK = 5000-300 = 4700 user cost UC = (r+d)Pk = (0.1+0.1)(1000) =0.2(1000) = 200 tax adjusted uc = uc/(1-/&tau) equilibrium: MPK = UC/(1-/&tau) => 4700=200/(1-/&tau) => 1-/&tau = 200/4700 = 0.0426 /&tau = 1-0.0426 = 0.9574 so tax adjusted UC = 200/(1-0.9574) = 200/0.0426 = 4694.835 b)![]()
3. a) Growth accounting formula: /&DeltaY/Y = /&DeltaA/A + /&alpha/&DeltaK/K + /&Beta/&Delta L/L so /&DeltaA/A = /&DeltaY/Y - /&alpha/&DeltaK/K - /&Beta/&Delta L/L = 6% - 0.3(2%) - 0.7(4%) = 2.6% (note: some bowsers don't support the code used here for the lower case greek letters capital delta, alpha and beta. If you see the symbols /&Delta /&alpha /&Beta they should be the upper case greek letters Delta, alpha and Beta.)b) Nominal GDP 1997 = 674.8 => Real GDP 1997 = 100x(674.8/121.6) = 554.93 Nominal GDP 1998 = 688.4 => Real GDP 1998 = 100x(688.4/123.3) = 558.31 -> Inflation rate = 100x(123.3-121.6)/121.6 = 1.398% -> Growth rate of real GDP = 100x(558.31-554.93)/554.93 = 0.61% c)(1)Uncertain/false: Spvt + Sgovt = I it could be financed by private or gov't savings (2)False: Unemployment rate = # of unemployed/labour force when workers are discouraged and drop out of labour force, both the numerator and denominator drop. The unemployment rate generally falls. However, employment rate = employed/working age population so as discouraged workers are already in the working age population, this figure is unlikely to change. (3)False: If constant returns to scale then the demand curve of labour is horizontal. This implies that MPL is the same for all L.