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Economics 146, Winter 2022

Homework #1

 

1(i)  Suppose that consumers must decide on how much to consume in each of two periods.  Suppose that the utility function in each period is given by:  U = 50 + 10C.  In other words it is 50 + 10C1 in period one and it is 50 + 10C2 in period two.  Also assume that households do not discount future utility of consumption (i.e. assume that the rate of time preference is zero).  Under these assumptions, do consumers prefer (10, 10) or (5,15) as the consumption path?  Explain your answer.  [hint: compute total utility over the two periods.]

(ii)  Do consumers prefer (10, 10) or (5,15) as the consumption path if the utility function in each period is lnC (where ln denotes the natural logarithm)?  If your answer differs from that in part (i), explain why.  (You may need a pocket calculator.)

(iii)  What is the preferred consumption path if the utility function in period one is lnC and is 2lnC in period 2?  Does your answer differ from that in part (ii)?  Explain.

 

2.  Based on our model of consumption demand that includes the real interest rate, r, as an explanatory variable, does aggregate current consumption increase when the actual rate of price inflation increases?  When people expect inflation to be higher in the future do they boost current consumption?  Which direction does the IS curve shift if the actual rate of price inflation rises?  What direction does the AD curve shift if the rate of price inflation rises?  

 

3.  Explain why it is plausible for the Fed's monetary policy rule to relate the real interest rate to the expected (rather than actual) rate of price inflation?  In other words, why is it plausible for the monetary policy rule to be:  r = r* + rπ πe ?  Would such an alternative monetary rule change the qualitative impact of exogenous demand and supply shocks on the main endogenous variable like real GDP and price inflation?  

How would your previous answers differ if the Fed's monetary rule related the real interest rate to the current GDP gap only?

 

4.  As stated in the lecture notes (p. 5) and in class,  Y = C + I + G + X – IM   is  equivalent to  I = Shh +  Sbus +  Sgov  +  Sfor.  Domestic saving (Sdom) is defined as: Shh +  Sbus +  Sgov  and net exports as:  X - IM = -Sfor.  If net exports are negative, as has been the case in the U.S. for nearly 30 years, is domestic saving less than or greater than domestic investment (I)?  Is the U.S. borrowing or lending to the rest of the world in this situation?

 

5.  Suppose that the Federal Reserve reduces real interest rates.  How does this affect aggregate demand?  Your answer should focus on a discussion of the traditional channels of influence of lower real interest rates on aggregate demand.  

 

6.  Using economic intuition, explain why the short run AS curve shifts upward when the expected rate of price inflation, πe,  rises.

 

7.  Empirically the correlation between price and inflation and the unemployment rate was negative from 1948 to 1971 but roughly zero for the entire post-war period.  It also was negative for the decade since the financial crisis began and positive for the 1970s, 1980s, 1990s, and 2000s.  Is the implied change in the correlation consistent with our macroeconomic model?  Explain. [There is no perfect answer but I want you to take on this admittedly difficult question.]

 

8.  Consider the Cobb-Douglas production function:  Y = AKα N1-α   where 0 <  α  < 1.

( i)  Viewing Kα as a constant (for short run analysis), how do the properties of this

function differ from the Blanchard model production function Y = AN?

 

(ii)   The elasticity of output with respect to employee hours worked (N) is defined as

 (dY/dN) / (Y/N) which is the ratio of the marginal product to the average product of

 labor.  Show that this elasticity equals 1 - α with Cobb Douglas production.

 

(iii)  The share of total income going to labor--known as labor's share--is defined as

SN  =  WN/PY where W is the nominal wage rate (per hour).  Show that the labor share

equals the elasticity of output with respect to employee hours assuming all firms operate

in perfectly competitive output markets and pay labor a nominal wage equal to the value

of its marginal product (note: this differs from wage determination in the Blanchard

model used in class).  Is the labor share pro-cyclical, counter-cyclical, or a-cyclical?

 

(iv)  Workers get paid their marginal revenue product (=MR x MPN) if firms are

 monopolistic.  What is the labor share, SN, in this case?  Is it greater or less than in the

previous case of perfectly competitive firms.  

 

(v)   The labor share, WN/PY, has declined very gradually over the post-WWII period in

the U.S. and declined a lot since the turn of the new century.  Can you explain why?

 

9.  Using the models developed in class, discuss the main short-run and long-run macroeconomic effects of firms having less pricing power (e.g. because of an increase in competition in output markets).  

 

10.  Starting from a position of full (long-run) equilibrium suppose something happens that leads us to observe a short-run (i.e., immediate) decline in price inflation and output but a rise in the real interest rate.  Explain what factor(s) could have caused these observations and why?  In addition to our observations on price inflation and output, suppose that the real interest rate declines (rather than rises); what factors could have caused this new set of observations?  

 

11.  Consider the two following U.S. business cycle facts:  (1) the real wage, W/P, is pro-cyclical and (2) price inflation tends to slow or decline during recessions.  

i.    Explain whether each business cycle fact is (or is not) consistent with the Keynesian/Blanchard model of business cycles.  

ii.   Explain whether each business cycle fact is (or is not) consistent with the Real Business Cycle (or Classical) model of business cycles.