ECO 3150 Study Guide - Pearson Education, Mutual Exclusivity, Collectively Exhaustive Events

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salmongoose831

14 Apr 2014

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P(a b) = number of outcomes satisfying a and b total number of elementary outcomes. P(a b) = p(a) + p(b) - p(a b) P(a) = na n n n = px. Cx x! n = cx n! x! (n - x)! n = Px n! (n - x)! x(x - 1)(x - 2)(2)(1) = x! n = ck n! k! (n - k)! Cx x! n = cx n! x! (n - x)! Statistics a tool to help process, summarize, analyze and interpret data. Population (n) the complete set of all items that interest an investigator. N can be very large or even infinite (cid:229) (cid:229) Sample (n) an observed subset of the population. Characteristics of a sample n represents the sample size. Sampling errors information is availiable on only a subset of all the population. Non sampling errors the population sampled is not the relevant one; survey respondents may give inaccurate answers; no responses to survey questions.

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2. Now you are told that the economy is producing efficiently and has chosen to produce and consume 8 units of X. At this point on the production possibilities frontier, you can use calculus to obtain the opportunity cost of Y as: A) 2 B) 1/2 C) D) 3/2 E) 2/3 F) 3 G) 1/3 H) 4 1) 1/4 J) 8/3 K) 3/8 L) 5/2 M) 2/5 N) 4/3 0) 3/4 P) 6 Q) 1/6 R) 8 S) 1/8 T) none of the above

Assume that the cost function for steel production is givenby the following expression:
(1) C(x,y) = F + c_xX + c_yY, wherec_j is the marginal cost of production of
type j steel, and X = output of X-steel and Y is output ofY-steel.
(a) Given this cost function, would it be possible for the steelproducer to sell the two types of steel at marginal cost and atleast break even?
Assume now that demands for the two different types of steel aregiven by
(2) X = A(px)^-e(py)^z andY=A(py)^-e(px)^z [these demand equations aretermed constant elasticity demand equations since the (e,z) do notdepend on the levels of prices]
In expression (2) above pâs are prices; A is a constant >0; e =own elasticity of demand; and z>0 is a cross-elasticity ofdemand between the two types of steel.
(a) Based on your general understanding of profit maximization,what is the minimum value for the elasticity e in eq.
(2) that has to be assumed to make the analysis make sense?
(b) Write down the profit function for the steel monopolist.
(c) Recall that the Lerner formula or condition states that(p-MC)/p = 1/E. Write down the profit maximization conditions forp_j j=X,Y. Can you write down the Lerner conditions forthe two products? Why is the formula different in this case fromthe usual formula? [Hint: analyze the implications ofcross-elasticity of demand on profit maximizing prices.] What wouldbe your answer is z=0?

ceruleanturtle953

Need help explaining PART C THANK YOU!

Suppose that two individuals, Jon and David, form a community and would like to construct a communal fort that would protect them from attacks. They both consume good X, a private good, and the protection of the fort, P. One unit of good X costs 1 unit of currency, and one unit of P costs 2 units of currency. Both Jon and David have an income of 100 and a utility function of the form:

U = log(X_i) + 2 Ã log(P_J + P_D)
The budget constraint for each is given by:
X_i + 2 Ã P_i = 100

(a) Find the amount of protection Jon will provide as a function of how much David provides, and explain why the relationship is the way it is.

(b) How much protection P will be privately provided in this case?

(c) Explain the economic intuition behind this amount, and compare it to the socially optimal amount without solving for the socially optimal amount.

HERE IS WHAT I DID SO FAR

A_ First you need to find the max utility, with is the utility and the budget constraint

U = log(X_i) + 2 Ã log(P_J + P_D) -> log(100-2PJ)+2log(PJ+PD)

Next you will need to differentiate the logarithim to get PJ

- 2 2

----------- + ----------------- = 0

100-2PJ PJ + PD

which we cal solve to generate

3PJ = 100 - PD

This can also be applied to PD

3PD = 100 - PJ

Using the substitute method we can find that (PJ = X; PD = Y)

3x = 100 - Y -> Y = -3x + 100

3(-3x + 100) = 100 - x

-9x + 300 = 100 - x

-8x = -200

x = 25

Which means that Y = 25

PJ = 25, PD = 25

25 +25 = 50

ECO 3150 Study Guide - Pearson Education, Mutual Exclusivity, Collectively Exhaustive Events

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