I.   Multiple Choice and True/False/Explain.   For multiple choice circle the letter which BEST answers the question. Read all of the responses before choosing your answer since “All of the above” may be the correct answer.   Multiple choice questions are worth 4 points each.   For true/false/explain clearly circle or state whether it is true or false and then explain in a few sentences.  Each true/false/explain question is worth 5 points:  2 points for choosing correctly and

3 points for explaining well.

1.   Consider a monopolist facing a market demand curve p(y) = 42 − y, and with a  marginal cost curve of: 2y + 2.  Markup is the price above setting MR=MC, that a monopolist charges: The amount of markup above the competitive price will be:

a.    $5 above perfect competition price

b.   $10 above perfect competition price

c.    $15 above perfect competition price

d.   $20 above perfect competition price.

2.    The total cost curve of a firm is TC = 2y2  + 10.  The variable cost curve of the firm is:

a.   VC = 2y2  + 10

b.   VC = 4y

c.   VC=10

d.   VC = 2y2

3.   The first fundamental welfare theorem of economics demonstrates that:

a.   Even in economies with externalities, the distortions are small enough that perfect competition leads to a pareto optimal distribution.

b.   Assuming perfect competition, consumers select goods that make them the best  off given all possible alternatives and producers to choose a production plan that maximizes profit over all possible alternatives.

c.   Assuming perfect competition, consumers select goods that make them the best  off given all possible alternatives while producers lack the incentives to choose a production plan that takes into account the consumer’s willingness to pay.

d.   Assuming perfect competition, consumers will become satiated on goods and        services even though market forces will drive producers toward increasing output.

True/False/Explain

4.   Consider the utility function from homework 5: u(x", x2 ) = x" "/2  + x2 "/2 .    Suppose p"  = 1, p2  = 2, m = 100.  True or false: when maximizing utility the consumer will    consume twice as much x"  as x2 .

Explain by solving for the mathematical relationship between x"  and x2 that always    holds when the consumer is maximizing utility. (hint: if you don’t remember the utility function in this problem is well behaved [that is convex and monotone]).

2.  Consider the following ordinary demand curve: X(p1, p2, m) = ;   p"  > p" . True or Fale X is a complement (based on prices) to good 2.  Explain, for full credit; explain by taking the appropriate derivative and discussing the signs.

Short Answer 1: Angel Grove. 18 Total Points.

imagined a city named Angel Grove that wants to prevent fire and crime.   When considering the consumption of police (X" ) and fire fighters (X2 ), the mayor has an income of $100, each police officer costs $10, each fire fighter cost $10.  Use these numbers for each subsection of this problem below (unless explicitly told otherwise in the subsection).

a.   Imagine that fire and crime are functions of the number of police officers and fire fighters respectively.  Specifically, Angel Grove experiences 10 crimes minus the   number of police officers and 10 fires minus the number of fire fighters.

i.           Write angel Grove’s budget constraint in terms of police (X" ) and fire fighters (X2 ). [3 points]

ii.          Write Angel Grove’s budget constraint in terms of the number of fires (F) and the number of crimes (C) rather than in terms of police (X" ) and fire fighters  (X2 ).  that angel grove “consumes.” [5 points]

iii.         Assume it is impossible for Angel Grove to have negative income. Note that   this means if the city wants zero crime (fires) it must accept a certain number of fires (crime).  Graph the consumption set and budget constraint below.      Shade the budget set of “affordable” bundles. [5 points]

iv.          Suppose both fire and crimes are “bads” for the town of Angel Grove.   Also assume the town has convex preferences. Draw a representative convex       indifference curve on your graph to ii. above.  Note there are many different indifference curves that could be correct here. Label the utility maximizing    point for the consumer on the graph (as point A) and draw the indifference  curve that goes through this point.  No need to solve for this optimal bundle exactly, just graphically chose the point based on the shape of the                   indifference curve. [5 points]

Short Answer 2.

2.  Producer Theory.  Total points: 20

The school cafeteria produces sandwiches (y) using labor (cafetieria workers) and capital   (bread/meat, ovens, the building).  The cafeteria’s technology is described by the following production function.    : y = l2/7C4/7 .

a.   Assume the price of a sandwich is p = $15.  In addition assume the cafeteria   workers hourly wage is w = $5.  Finally, let the price of capital be $2.  Fix         equipment at c=1 unit.  Next, I will ask you to go through the steps to solve Dr. X’s short run profit maximization problem.

i.   Find the marginal revenue product: p ∗ mpl : [5 points]

ii.   Set the marginal revenue product equal to the wage.  Solve for the       optimal amount of labor the cafeteria should hire in order to maximize profit. [6 points]

b.   Instead, imagine that we wanted to derive the cafeteria’s variable cost function. Beginning with the production function above (y = l3/5c 1/5), and the wage rate above: w = $5. Derive an equation for the variable cost curve.  [5 points]

c.    What term do we use for a firm who, as the sole company purchasing labor in a market, can use their market power to hold down wages below their efficient     level?  If the cafeteria workers in turn unionized and jointly refused to work        unless the cafeteria raised wages, what would we call that (alternatively, what   property do they have as an economic actor: in terms of how they engage in the market)?  [4 points]

Monopsony, workers in this case would be acting like monopolists or we could say they have market power/ worker power.

Short Answer 3: Demonstrating externalities using producer theory and game theory. [29 points total]

Consider a firm who produces a consumption good  (C) using a single input: water.  The amount of water the firm uses in production is denoted as: X .  The firm’s production function is: C =       f(X) =  X .  Water is a free resource which costs nothing for the firm to use (HINT: this means the cost of the input is zero). However, there are only 10 total units of water available in this      economy. That is: X ≤ 10. Further every unit of water used in production turns that water into a unit of slimy sludge.

a.   Below is a graph of the production function. Assume the price of the output is    p = 1. Given that water is free, draw a representative iso-profit line on the graph below.  With this Iso-profit line in mind: indicate the firm’s profit maximizing    choice of y and X on the graph below. Label this point A. [5 points]

b.  Now let’s more formally model how to solve for the optimal amount of water pollution. Given the firm’s production function above: C = f(X) =  X. Assume the consumer has the utility function: U(C, X) = C − 3X"/3  .  Agiain, assume the price of the output is p = 1.

Note that because it is costless for the firm to produce c, and because the price of the output is 1, the marginal profit of producing one more unit is equal to the marginal   physical product of the firm.  This idea helps us set up the solution to the problem.

bi. In terms of this model, how would we go about finding a socially optimal level of pollution?  Do we desire there to be zero pollution in the economy, why or why not:  how is this reflected in the equations in the model (explain in words)? [5 points]

We set the marginal benefitsfrom producing (in terms of profit or utility) a unit of the consumption good equal to the marginal cost ofpollution. Typically we don’t desire   there to be zero pollution: because pollution benefits consumers through allowing the production of the consumption good.  Wejust want thefull social costs ofpollution to be taken into consideration. This is reflected in the above equation where pollution is used to produce the consumption good which goes directly into the utilityfunction.

Bii.  are two ways I can think of to set up the “problem” of pollution facing society.   One is to specify a social welfare function: where a beneficent social planner              recognizes that a firm benefits from the profit from polluting water while also            recognizing that the consumer suffers the negative consequences.  Another way to set up the problem is to imagine the case where the consumer owns the firm and directly consumes any of the consumption good the firm produces.  Try writing down both     equations below. [5 points]

Bii.  Using one of the two equations above, solve for the optimal level of pollution (x) in the economy by setting the marginal benefit from pollution equal to the marginal    cost; and finding the optimal level of x. [5 points]

c.   Now look back at the graph you drew in part a. above. In class we learned that a               Pigouvian tax is one tool to correct for an externality.  Remember: a Pigouvian tax is a     tax applied to a firm that produces a negative externality that shifts the supply curve to be in line with the marginal social cost curve.

Given the above graph and the equation for Imagine the government levied a quantity tax per unit of water used.  Denote the amount of this quantity tax as t .

i.          Given that the production function reflects constant returns to scale, at what value of t would it be the case that the firm would not have an incentive to pollute more or less? That is, what tax would cause a firm to stay at their current level of          production and not use more water (turning it into sludge) or less water.                Remember, the price of the output is: p = 1.  [5 points]

ii.        Provide a value for  t at which the firm would shut down.  Ie. a  t that is high enough such that the firm always chooses to produce y = 0. [3 points]

iii.       Extra Credit for 2211Q students required for 5201/MA students  [up to 4    points] Given the utility function for the consumer above, would the consumer  prefer there to be no tax on the use of water (t = 0) .Or a tax on the use of water such that the firm shuts down?  Explain by referring to the utility function.  As a reminder, the consumer’s utility function was: : U(C, X) = C − 3X"/3

Very short answer 4.  Game Theory

Both Guilder and Florin must choose between sending their fleets to fight at either the big pirate outpost or the small pirate outpost (at this point ignoring the pirate threat and staying home is not an option). Neither nation knows what the other nation will do.  If they both attack the small       outpost they are guaranteed a complete victory against the pirates at this output.  In this case,       they will each receive a payoff of 300 gold coins.  If they both attack the big outpost, they will    also be successful, but will sustain heavier losses as well.  In this case they each will each only    receive a payoff of 150.  If they go to different outposts they are completely defeated, and the      payoff for both of them is -50.

4.a. Write out the payoff matrix for the above simultaneous game.  The matrix should make clear the players, strategies, and payoffs. [6 points]

4.b.  Find the Nash Equilibrium and dominant strategies for this game (if there are any).  [6 points]