Lectures 8&9: General Equilibrium Nicolas Roys University of Wisconsin Madison Econ 302
Topics Closed-Economy One-Period Macro Model Experiments: ncrease in Governements Expenditures Government Expenditures during World War ncreases in total factor productivity Applications: Evolution of hours worked Evolution of leisure
Closed-Economy One-Period Macro Model Putting everything together: Representative Consumer decides how much to work and how much to consume: (c, N s ) taking as given the wage rate Representative Firm decides how much to produce Y and how much labor to hire N d taking as given the wage rate Government raises lump sum taxes T and spends G Static world: K = K constant
Why? We will now put these together. Why? 1. Consistency: we are sure that everyone is doing things that are compatible. what is produced in the economy is determined entirely by the interaction of consumer preferences with the technology available to them. 2. To derive positive predictions from the model 2.1 impact of government expenditures 2.2 impact of technological progress
Exogenous Variables Exogenous Variables: K, G and z. Endogenous objects: w, N, c, T, Y,,l. EXOGENOUS VARABLES P of Tea, ncome Weather, #Firms ECONOMC MODEL ENDOGENOUS VARABLES P and Q of Coffee
Competitive Equilibirum ACompetitiveEquilibriumis 1. an allocation {Y, N, K, c} 2. apricesystem{w} 3. agovernmentpolicy{t, G} such that 1. Consumer optimizes given market prices: (N s, c) 2. Firm optimizes given market prices N d 3. The government budget constraint is satisfied G = T 4. Markets clear: Goods Market Y = zf (K, N) =c + G Labor Market N d = N s
ncome-expenditure dentity n a competitive equilibrium, the income-expenditure identity is satisfied, so Y = C + G Why?
ncome-expenditure dentity Consumer s Budget constraint: C = wn s + T Profits: = Y Governement Budget Constraint: wn d T = G
ncome-expenditure dentity Consumer s Budget constraint: C = wn s + Y wn d G +Equilibrium on the Labor Market done!
Solving for an Equilibrium Graphical Approach key here: find w to clear labor market
Production Function Production Function Time Constraint So Y = zf (K, N) N = h l Y = zf (K, h l)
Production Possibilities Frontier n Equilibrium Combined with Finally: C = Y G Y = zf (K, h l) C = zf (K, h l) G Definition The Production Possiblities Frontier describes what the technological possiblities are, for the economy as the whole, in terms of the production of consumption goods and leisure
The Production Function and the Production Possibilities Frontier
Key Properties of a Competitive Equilibrium From consumer utility maximization: MRS l,c = w From firm profit maximization: MP N = w mposing labor market clearing: MRS l,c = MP N
Competitive Equilibrium
WW and ncrease in G During WW government spending to finance the war effort increased to levels unseen previously in the US. What are the predictions of the model for this increase in spending? The assumption that government spending is a loss of output arguably makes sense here. Military expenditures protect us But means less consumption goods and services
ncrease in G
ncrease in G Essentially: Negative ncome Effects increase in (Y, N) decrease in (c, w). Private consumption spending is crowded out by increased government spending. loss of welfare as both c, l fall. Crucial Assumption: G is not in the Utility Function These predictions match US experience of WW.
WW2 Large ncrease in Government Expenditures Yincreases, Cdecreasesbyasmallamount.
What Does This Analysis Miss? Government debt. Alargefractionofthewartimespending was financed by government debt. Deficit/GDP ratio hit 24% by 1944. So Taxes increased less which is maybe why consumption only decreased by a small amount ncreased productivity. Wartimemobilizationofproduction increased labor productivity dramatically. ncrease in Output is larger than our model suggests
Fiscal Multiplier Fiscal Multiplier= Y G n current discussions of fiscal stimulus, the size of the multiplier a source of some controversy. Obama administration suggests 1.5 Barro suggests 0 Our model says: effect on GDP < 1becauseofcrowdingout. This isn t the best framework for current issues, as there s no unemployment or idle resources. These are the main rationale for the fiscal stimulus.
TFP
TFP
TFP 2Effects: Substitution Effect: Shift down the new Production Possibilities Frontier ncome Effect Total Effect: C increases unambiguously Effect on N will depend on income and substitution effects Y increases w increases Substitution: move along the same indifference curve with less leisure: higher MRS c,l ncome Effect: more leisure - less employment: higher MP n
TFP Remember that z is technological progress The model predicts that technological progress leads to more consumption, more output, higher wages and ambiguous effect on number of hours worked We know that z has been increasing over time in the data. Let s see whether we observe the predicted trend in endogenous variables in the data. Y t = z t K 1 3 t N 2 3 t Take the US, we can recover z t since: Y t :realgdpinyeart K t :stockofcapitalinyeart N t :totalhoursworkedinyeart
Figure: Level of Technology z t Figure: Real GDP per capita y t
Figure: Real Consumption per capita c t Figure: Real hourly wage per capita w t
TFP So data seems consistent with this VERY simple model Really? Let s Examine Changes in Hours Worked in the US since 1950. Hours worked per person have been roughly constant since WW overall:+7% from 1950 to 2000 (an order of magnitude smaller than changes in output, consumption...)
Hours Worked per person 10 15 20 25 30 35 1950 1960 1970 1980 1990 2000 year Hours per person: All Hours per person: Female Hours per person: Male
Hours per person Hours per person = Total Hours worked Population = Total Hours worked Labor Force Labor Force Population = Hours per worker Participation Rate 1. ntensive Margin: Hours per worker 2. Extensive Margin: Participation Rate
Hours per worker 34 36 38 40 42 44 1950 1960 1970 1980 1990 2000 year Hours per worker: All Hours per worker: Female Hours per worker: Male
Participation Rate 30 40 50 60 70 80 1950 1960 1970 1980 1990 2000 year Participation Rate: All Participation Rate: Female Participation Rate: Male
Changes in Hours Worked Hours worked per person have been roughly constant since WW overall:+7% from 1950 to 2000 Hours per worker: -4.5% total population Large reallocation of working hours from males to females is almost entirely due to the changes in the fractions of these populations that are employed, with females becoming employed more and males becoming employed less Participation Rate of Men: -15% Participation Rate of Women: +87%
ncrease in Leisure in the US Mark Aguiar and Erik Hurst document trends in time allocation in the US: Leisure l increased dramatically in last 40 years: between 4-8 hour a week (for somebody working 40 hours a week: that is equivalent to 5-10 weeks of extra holiday a year) Time constraint augmented with non-market work M: Decomposition: l + N + M = h N: hoursworkedinthemarketsector l: socialactivities,entertainment,televisionwatching,sleeping M : meal preparation, doing laundry, household cleaning, grocery shopping, going to the bank/postoffice,...
Men s Time Allocation (Change Relative to 1965)
Women s Time Allocation (Change Relative to 1965)
ncrease in Leisure in the US men: l increase offsets a decrease in market hours N 5hoursperweekincreaseinleisure increase their time spent on non-market hours by 4 hours per week large decrease in hours per person women: l increase offsets a decrease in non-market hours M 4hoursperweekincreaseinleisure 10 hours decline in non-market hours mproved technology in home sector (appliances, home delivery, the nternet, e-shopping) may explain M drop for women