Try to work these on your own, but feel free to discuss these with other students, Nazmi or me if you want.
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1.  Add or subtract the following linear functions:

• Y = 2 + 4X  plus  Y = 4 + 2X             just add correcponding terms: 2Y = 6 + 6X  or  Y = 3 + 3X
• Q = 5 - 2P  plus  Q = -2 + 0.5P          2Q = 3 - 1.5P  or  Q = 1.5 - 0.75P
• TR = 10Y  minus VC = 0.05Y^2 minus FC = 20        Profit = 0.05Y^2 + 10Y  - 20

2.  Between 2000 and 2003 the price of a small pizza increased from $5.00 to $6.00, and the price of a liter of soda stayed the same at $1.25. 

• In 2000, Filbert consumed 5 pizzas and 10 liters of soda per week.  Using 2000 as the base year, calculate the cost index for Filbert's 2000 consumption bundle in 2003.    
  Exp2000 = $5/pizza x 5 pizzas + $1.25/soda x 10 sodas = $37.50
  Exp2003 = $6/pizza x 5 pizzas + $1.25/soda x 10 sodas = $42.50
  Lespeyres Index = 100 x $42.50/$37.50 = 113.3
  
• In 2003, Filbert (who still hasn't graduated) is actually consuming 4 pizzas and 13 liters of soda per week.  Using 2000 as the base year, calculate the cost index for Filbert's 2003 consumption bundle.
  Exp2000 = $5/pizza x 4 pizzas + $1.25/soda x 13 sodas = $36.25
  Exp2003 = $6/pizza x 4 pizzas + $1.25/soda x 13 sodas = $40.25
  Paasche Index = 100 x $40.25/$36.25 = 111.0
  

3.  Invert the following equations (solve for the right-hand side variable in terms of the left-hand side variable):

• Q = 100 - 0.25P            0.25P = 100 - Q;  P = 400 - 4Q
• Y = 32.6 + 0.54X          0.54X = Y - 32.6;  X = 1.85Y - 60.37
• MC = -10 + 0.05Y^2    0.05Y^2 = MC + 10;  Y^2 = 20MC + 200;  Y = (20MC + 200)^0.5

4.  If  a monopolist is selling in a market with demand Q = 64 - 2P, calculate the price elasticity of demand and the monopolist's total revenue (P x Q) where...    Some quick review here: being the only seller in the market, the monopolist faces the entire market demand schedule.   If he wants to sell more, he must cut his price to everyone (he can't get away with price discrimination, charging different buyers different prices).  So a monopolist only sells in the elastic portion of the demand schedule, where the percent increase in quantity sold is greater than the percent decrease in price he can charge.  Elasticity = dQ/dP x P/Q, and in this problem dQ/dP = -2 (the slope of the demand schedule).  Invert the demand schedule (P = 32 - 0.5Q), plug in each Q and solve for the corresponding P.  Then...

• Q = 20     P = $22;  E = -2(22/20) = -2.2;  TR = PQ = $22 x 20 = $440
• Q = 30     P = $17;  E = -2(17/30) = -1.13;  TR = $17 x 30 = $510
• Q = 40     P = $12;  E = -2(12/40) = -0.60;  TR = $12 x 40 = $480
• Q = 50     P = $7;  E = -2(7/50) = -0.28;  TR = $7 x 50 = $350

5.  Solve the following supply-demand equations to determine the market equilibrium point:

• Q(demand) = 200 - 0.25P    Q(supply) = P - 25      200 - 0.25P = P - 25;  225 = 1.25P;  P = $180;  Q = 155.
• Q(demand) = 16.7 - 0.0012P     P = 0.05Q(supply) + 2    Q = 16.7 - 0.0012[0.05Q + 2]; 16.6976 = 0.99994Q;
                                                                                             Q = 16.6986; P = $2.83493
  

6.  You are using a spreadsheet to model a single-input producer, and have the following spreadsheet fragment:

  |   A   |   B   |   C
  ------------------------
1 |P(X)=   P(Y)=   FC=
2 |  $7.00   $4.50  $50.00
3 |
4 |      X       Y    
5 |      0       0
6 |      1       2
7 |      2       5

What spreadsheet formulas would you enter in Row 6 for each of the following?

(column C) MPP  =(B6-B5)/(A6-A5) (column D) APP   =B6/A6 (column E) MVP   =$B$2*C6  or  =$B$2*(B6-B5)/(A6-A5) (column F) MFC   =$A$2 (column G) TR      =$B$2*B6 (column H) VC      =$A$2*A6

(column I) TC       =H6+$C$2 (column J) ATC    =I6/B6 (column K) MC    =(I6-I5)/(B6-B5) (column L) MR     =$B$2  or  =(G6-G5)/(B6-B5) (column M) Profit  =G6-I6

• How will an increase in P(X) affect the profit-maximizing levels of X and Y?  Explain.
  It shifts MFC upward, shifting the MVP=MFC intersection to the left, reducing X;
  It shifts MC upward, shifting the MR=MC intersection to the left, reducing Y.
  
• How will an increase in P(Y) affect the profit-maximizing levels of X and Y?  Explain.
  It shifts MVP upward, shifting the MVP=MFC intersection to the right, increasing X;
  It shifts MR upward, shifting the MR=MC intersection to the right, increasing Y.
  
• How will an increase in FC affect the profit-maximizing levels of X and Y?  Explain.
  It has no effect on optimal X or Y!  
  

7.  Suppose you used a really primitive regression package to regress quantity of chicken demanded (Q) against price per pound (P), and obtained the following regression output.  The model being tested is Q = a + bP, and the hypothesis for coefficient b is that b<0.  

SUMMARY OUTPUT
R Square          0.425    (means the model explains 42.5% of the variation in Q)
Observations      21
             Coeffs StdError    
Intercept    17.12  6.40    t = 17.12/6.4 = 2.6875 (significant at 99% level)
P (price)    -0.64  0.41  t = -0.64/0.41 = 1.560976 (not even significant at 90% level)

• Calculate the t-statistics for the Intercept and Price coefficients (divide the coefficient value by the StdError).  
• Analyze the statistical significance of each coefficient based on its t-statistic.  How well does this model support the hypothesis that b<0? More formally, does this model REJECT the null hypothesis that b is NOT negative at the 95% or better confidence level?  
  This model "fails to reject the null hypothesis" that demand does NOT respond to price with even 90% certainty.
  
• What percent of the total variation in quantity demanded is explained by this model?
• If it takes two observation points to even define the line (slope and intercept), how many additional observation points ("degrees of freedom") are contributing residual variation that lets us compute statistical significance?  
  Of 21 observations, 2 "define" the line; the remaining 19 "degrees of freedom" contribute variation.
• Calculate the point elasticity of demand where Q = 10.  
  The empirical model is Q = 17.12 - 0.64P, or inverted, P = 26.75 - 1.5625Q, so if Q = 10, P = $11.125;
  E = (dQ/dP)x(P/Q) = -0.64($11.125/10) = -0.712
  

8.  Suppose you regressed quantity of golf balls demanded against the price of golf balls, greens fees, price of tennis rackets and income:
Q(golfballls) = a + b1*P(golfballs) + b2*P(greensfees) + b3*P(tennisrackets) + b4*Income.
What signs would you expect for each of the b coefficients?  Explain.
b1 < 0  (demand for golf balls should decline as price of golf balls increases)
b2 < 0  (this is a complementary relationship: as greens fees rise, people play less golf and buy fewer golf balls)
b3 > 0  (tennis is a substitute for golf)
b4 > 0  (golf is a normal good)

9.  When an economist refers to children as "inferior goods," what does she mean?  When she calls health care a "luxury good," what does she mean?  
An "inferior" good is simply any good that people consume LESS of as their incomes increase.  Rich people tend to have fewer children than poor people, and rich nations have lower fertility rates than poor nations.
 A "luxury" good is simply any good that people spend PROPORTIONATELY MORE of their incomes on as their incomes rise.  Rich people tend to spend a higher percent of their incomes on health care than poor people.

10.  If a firm's total profit function is PROFIT = -100 + Y - 0.001Y^2,

• What is its MARGINAL profit function (the derivative of the total profit function)?    MargProfit = 1 - 0.002Y
• Solve this marginal profit function for the output level Y* where marginal profit equals zero.    1 - 0.002Y* = 0;  Y* = 500
• What is the firm's total profit at the output level where marginal profit equals zero?  Explain why this output level yields the maximum TOTAL profit.    at Y* = 500, Profit = $150.   Marginal profit is the slope of total profit.  The point where marginal profit=0 corresponds to the point where total profit reaches a peak.  (To check: if Y = 490, profit = $149.90;  if Y = 510, profit = $149.90)