San Francisco State University ECON 302 Fall Problem set 2 - Solution

Transcription

1 San Francisco State niversit Michael Bar ECON 302 Fall 206 roblem set 2 - Solution NIA. 5 oints. The net table resents actual data collected b the Bureau of Economic Analsis in All numbers are in billions of dollars. ersonal Consumtion Eenditures Gross Investment Government Consumtion Eenditures Net Eorts -624 Comensation of Emloees Net Interest Rental Income 34.2 rorietors income Cororate rofits Indirect business ta net of subsidies Consumtion of fied caital Statistical Discreanc a. Based on the above data calculate the GD using the eenditure aroach. GD C + I + G + NX b. Based on the above data calculate the GD using the income aroach i.e. calculate the Gross Domestic Income. GGGGGG WW + IIIIII + RRRRRRRR + ππ + ππ BB + TTTT + DDDDDD c. Verif that the two measures of GD differ onl b the magnitude of the statistical discreanc. GGGGGG + SSSS GGGGGG oints. The net table rovides data on rices and outut in some artificial econom for the ears The goods are labeled and 2. See the illustration osted on the course web age for hel. For all the questions it is recommended to use Ecel.

2 Year Q 2 Q2 Year a. Construct the series of GD real GD Q Imlicit rice Deflator growth rate of real GD gq growth rate of g using the base ear aroach when the base ear is In other words comlete the table below. Year Q 2 Q2 GD Q gq g b. Reeat art a when the base ear is Year Q 2 Q2 GD Q gq g c. Decomose the growth in nominal GD between 2004 and 2005 into the growth of real GD and Inflation when the base ear is 2000 and when the base ear is Base 2000 GD2005 Q2005 GD2004 Q Base 2005 GD2005 Q2005 GD2004 Q

3 d. What did ou learn from this eercise Does the choice of the base ear matter the resulting growth in real GD and inflation? When using the base ear method the choice of the base ear affects the decomosition of growth in nominal GD into real GD growth and inflation. In this eamle when the base ear was chosen to be 2000 real growth of about 7% and inflation of 4% but with 2005 as base we have real growth of 3% and inflation 8% oints. For this question ou need to use the Data for HW2 on the course web age. a. lot the grah of ersonal consumtion eenditures as a ercentage of GD. ercent C/GD 90% 80% 70% 60% 50% 40% 30% 20% 0% 0% Time b. lot on one diagram the grahs of consumtion of durable goods as ercentage of ersonal consumtion eenditure 2 consumtion of nondurable goods as ercentage of ersonal consumtion eenditure and 3 consumtion of services as ercentage of ersonal consumtion eenditure. 3

4 ercent ercentage of Durable Goods Nondurable Goods and Services in ersonal Consumtion Eenditures 80% 70% 60% 50% 40% 30% 20% 0% 0% Time Dur/C NonDur/C Serv/C Micro Foundations 4. 0 oints. Consumer choice model. a. Consider a model in which the consumer chooses otimal consumtion of XY. Draw a diagram of a tical budget constraint and indifference curves and show the otimal consumtion bundle. Y Otimal consumtion Bundle X b. Write the mathematical condition for otimalit of consumtion bundle and give a verbal interretation of the condition. 4

5 5 The condition for otimal consumtion bundle: Interretation : The left hand side is the sloe in absolute value of the indifference curve and the right hand side is the sloe in absolute value of the budget constraint. Thus at the otimum indifference curve and the budget constraint must be tangent. Interretation 2: The above condition can be written as The left hand side is the utilit generated b etra dollar sent on X and the right hand side is the utilit from etra dollar sent on Y. The otimal allocation of income between the two goods requires that those should be the same oints. Consumer choice model with Cobb-Douglas references. a. Suose that consumer s utilit is given b 0 < <. The rices of goods X and Y are Y X and his income is I. se the Lagrange method to derive this consumer s demand for the goods X and Y. The Lagrangian is: ] [ I L + Ste : First order conditions: L L Ste 2: Dividing b 2 gives Ste 3: Solving for : Ste 4: lugging into the budget constraint:

6 Which gives the demand for X: And from ste 3 the demand for Y: + I + I I I I b. Based on our answers in a what haens to the demand for X and Y if income goes u? The demand for both goods goes u as income goes u. This means that both goods are normal. c. Based on our answer in a what haens to the demand for X and Y if X goes u? The quantit demanded of X will decrease while the demand for Y will not change. d. Based on our answer in a what haens to the demand for X and Y if Y goes u? The demand for X will not change while the quantit demanded of Y will decrease. e. Based on our answer in a what haens to the fraction of income sent on X Y if the Income or rices change? The fraction of income sent on each good is fied and indeendent of income and rices. We see from the demand equations that the consumer will alwas send a fraction of his income on X and the remaining fraction a on Y. f. Reeat art a for ln + ln 0 < <. The Lagrangian is: L ln+ ln [ + Ste : First order conditions: I] 6

7 L 0 L Ste 2: Dividing b 2 gives 0 2 This is the same first order condition for otimal bundle as the one obtained at the end of ste 2 of section a. The rest of the stes are thus identical to art a. Ste 3: Solving for : Ste 4: lugging into the budget constraint: + I + I I Which gives the demand for X: I And from ste 3 the demand for Y: I g. Elain wh did ou get the same demand in arts a and f even though the utilit functions are different. The utilit function in art f is a logarithmic transformation of the utilit in art a. In art a: In art f: V ln ln ln + ln We have shown in class that aling a monotone increasing transformation to a utilit function creates a different utilit function but the new one reresents the same references. In other words suose that consumer A has utilit and consumer B has utilit V ln + ln then the have the same references and thus will make the same choices and will have the same demand. Formall we sa that utilit functions are invariant with resect to monotone increasing transformations. 7