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ECON203 Intermediate Microeconomics

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Course Code: ECON203
University: University Of Victoria

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The problem sets are personalised. Each student will have an individual set of numbers assigned to them. The problem set questions will require you to substitute values of particular numbers from your individual set for parameter values in the question. This means that every student will essentially have a different set of problems to complete. Although pooling of knowledge is desirable for improving understanding, keep in mind that a) the usual Academic Integrity requirements apply in relation to submitting only work that is entirely your own, and b) in some cases differing parameter values might cause your problem solutions to be qualitatively different from that of your peers.
Problem solutions must be submitted in pdf form via the supplied links, preferably typed. If not typed then solutions must be completed in a highly legible form. Submissions written in hieroglyphics or alien languages, or in sizes suited to microfilm might not be marked.
Quite often the solution method to problems will be contained in worked examples in the textbook. Where not, suitable hints will be provided publicly. Some additional background information relating to mathematical methods will also be provided.
A Microeconomic Analysis of Institutions. Department of Economics,
The Microeconomic theory of the Rebound Effect and its Welfare Implications.
Theoretical Analysis of Microeconomic Effect of Public Investment. Asian Journal of Economic Modelling.
Does the Entrepreneurial Human Capital is Important for Organizational Performance?
E-Commerce Adoption and Analysis of the Popular E-commerce Business Sites in Malaysia.


Question 1
From; U= X21 X12, Agent’s income, Y= 19.  Price of good 1, P1=6, price of good 2, P2=4,
Budget constraint, B=6 X1+4X2=19, Demand functions for good 1 and 2,  the equation becomes;
Z= X21 X12+ ? (19-6 X1-4X2), Taking first order differentiation we get;
dZX1= 2 X21 X12-6 ?=0……………………1
dZX2= X21-4 ?=0…………………………….2
dZ?=19-6 X1-4X2=0
  19=6 X1+4X2……………………………….3
Combining equations 1 and 2 gives;
X21/4=1/3(X1 X12), Dive both by X1
X1/4=1/3 X12, X1=4/3 X12………………………………………4
Also;X2=3/4 X1…………………………………………5
Substituting equations 4 and 5 into 3 to get the respective demand functions gives;
For good 2
19=6(4/3 X2) + 4X2
X2=19/12; but 19=Y(income)
Therefore, demand function for good 2 is, X2=Y/12.
Good 1
Also, from 19=6 X1+4(4/3X1)
19=6 X1+3 X1,   X1=19/9; but 19=Y(income), Therefore, the demand function for good 1 is X1=Y/9
The quantities of good 1 and 2 are;
From X2=Y/12, X2=19/12,  X2=1.58 units
Therefore, 1.58 units of good 2 are being demanded.
Also; from X1=Y/9, X1=19/9, X1=2.11 units
Therefore, 2.11 units of good 1 are being demanded.
Question 2.
Given is, U= X41 X22, Agent’s income (Y)= 36, price of good 1, P1=8 and price of good 2, P2=4
Forming the equation; BL=8 X1+4X2=36
Z= X41 X22+ ? (36-8 X1-4X2) and taking first order condition and equating to zero;
Z1= 4X31 X22-8 ?…………………………………….1
Z2= 2X41 X2-4 ?………………………………………2
Z ?=36-8X1-4X2………………………………………3
Combining equations 1 and 2 we get;
1/2X31 X22=1/2X41 X2, then, dividing both sides by ½ X2 gives
X12=X22, Hence, X1=X2 and   X2=X1
Considering the demand fiction for good 1 whose price increased to 8;
36=12X1, X1=36/12=3 units

The total price effect.

This measures the impact in the value of the consumer demand for goods and services in the market. It can also refer to the overall impact the event has on product’s price (Stocker 2018). The total price effect consists of the substitution effect and the income effect as described below. It shows the change of the consumer in his optimal consumption bundles (Shobe 2018).
When the consumer’s optimal consumption bundles are situated on the high indifference curve, he is better off consuming that particular combination. Similarly, he is worse when his combination falls below the indifference curve (Amin 2018). Keeping the price of other goods and income constant, the price effect finds how much the consumer’s satisfaction varies especially when the price of one commodity changes. When the consumer understands the price change, his response always varies with the nature of the commodity in the question, that is to say; if it is a normal good, neutral good or even an inferior good.

The substitution effect.

The substitution effect shows how much the consumer has substituted one good for the other in case there is a change in consumption of the good (Balal e t al 2018). In most cases this change is brought about by different behaviors such as increase or decrease in price and change in tastes and preferences.
From; ΔX14=X1(P’ 1 Y’)-X1(P1 Y), There is need to find out how much has to be changed on the consumer’s income to make him consume the original units without affecting his welfare when the price was initially at 6.
Using; ΔY=X1ΔP1=2.11(8-6) = 4.22
Thus, the consumer’s income will be increased by 4.22 to keep his purchasing power following an increase in the price.
Hence; M’= M+ΔM=19+4.22=23.22, meaning that if his income was 23.22, then, the Agent could continue to purchase his bundle of goods (Asirvatham 2018).

The income effect.

From the calculation above; the initial demand for good 1 was initially 2.11 units. With a price change to 8, the new demand for good 1 is 3 units. The total change in demand is 3-2.11=0.89 units. It follows that with a change in the price of good 1, resulted into a small increase in its demand, hence this good 1 is a necessity good (Bashir, 2018). Such goods have inelastic demand such that any change in price results in a corresponding change in its demand.
Question 3.

Laspeyres measure of the welfare change

A Laspeyres price index as a measure of welfare change, which shows how the consumer’s cost of a particular buddle changes say from the base period 0 to the time t (Shobe 2018). It identifies how the consumer’s (Agent) welfare will change in a given time period given the price of one commodity has changed (Chin e tal,2018). However, the index has some weaknesses such as; it works on the assumption that consumers don’t react to changes in the prices of the commodities. So, it is unrealistic since it ignores the fact that consumers can always substitute the goods (Amin 2018). That is to say, buy more of commodities as the price reduces and buy less when there is an increase in price.

Paasche measure of the welfare change.

The Paasche measure uses the current period in which the change has occurred. An increase in the price of good 1 will lead to a decline in quantity demanded for that particular good. It helps to monitor the consumer changes in welfare with respect to changes in prices (Stocker 2018).

Compensating variation.

Compensating Variation makes an adjustment in consumer’s income to return to his original level of utility when an economic change say price change has occurred. The maximum the consumer is willing to allow the economic change happen varies with the type of the change (Abdali 2018). For example, a fall in price of the good 1, makes the consumer (Agent) willing to pay for the commodity to allow change happen. While in cases where there is a negative change say a rise in price as above (price of good 1 increased to 8) consumers or Agents are not willing to pay to allow the economic change. Here the compensating variation is the minimum value to which the consumer will need to allow the change happen.

Equivalent Variation

Equivalent variation measures the improvement in the consumer’s (Agent’s) income which changes his level of utility equal to the level that would have occurred if at all the change happened. It measures how income is adjusted to meet the changes in consumer’s utility. Following the rise in price above as the negative change, Equivalent variation shows the amount of income needed to be taken away so as the Agent’s level of utility lowers.
 A rise in the price of good 1, causes the agent to change his consumption bundles. Therefore, Equivalent variation measures how much is needed to increase his income to have the same welfare as before the increase in the market price (Nathan and Gillingham 2015).
Question 4.

The ordinary demand curve illustrates how the agent of consumers will purchase commodities at a given price level (Olsson 2015).

From =(X1X2) + e (1, 9)
(X1-e1)=(10-1, 9) +(10, 1-9) …………………1And, (X2-e2) =(9-1, 10) +(10, 1-10) ………2
Equations 1 and 2 are ordinally demand functions for good 1 and 2 respectively.
Gross and net demand2 for good 1 and 2
Two good model is given by; {X1 X2}, Endowment {e1 e2} = (1, 9) {X1, e2} = {10, 9}……………1
{(X1-e1, X2-e2} = {10-1, 1-9)} = Net demand ……………………….2
Therefore, equation 1 and 2 are the gross and net demands respectively.
But also; when, X1-e1>0, demander of good 1 (Gaprindashvili 2018).
                             X2-e2<0, supplier of good 2. Full insurance occurs where the insurer pays exactly what he or she insured with the company (Dada 2015). From the utility function; U=W0.5/2=W0.25 Max(U) = 0.25W0.75 But prob that he will be robbed, P = 0.025. Wealth that is robbed = 6000 Then, full insurance will equal, P*MaxU = (0.025*0.25(6000)0.75)19000 =80955.63 Therefore, the full insurance is 80955.63 Actuarially fair premium is equal to the expected costs and these are calculated as follows; Ec=P*(loss of wealth/ being robbed) + (1-P) (not robbed)     = 0.025(6000) +0.975(19000)     =18675 Hence, his actuarily fair premium is 18675 Question 5. UA= X12X42 Endowments, e(X1,X2) = e(3, 6) UB = X18 X42, e(X1,X2) = e(6, 3) and equilibrium occurs when both agents demand for good are equal, P1(X1, e1) = P2(X2, e2) P1 (9-3) = P2(9=6), 6 P1 = 3 P2,  P2= (4*6)/3, P2 = 8. Therefore, the equilibrium price of good 2 is 8 (Mankiw 2014). Gross and net demands Agent A, {X1, e2} = {9, 6} …gross……………………1 {X1-e1, X2-e2} = {9-3, 1-6} = net demand………...2 Therefore, equations 1 and 2 are the gross and net demands for agent A. Agent B, X1, e2} = {9, 3} …gross……………………* {X1-e1, X2-e2} = {9-6, 1-3} = net demand………** Hence, equations * and ** are the gross and net demands for the agent B UA= X18 X24 Equilibrium occurs when the demand for goods is equal,  e (6, 3), P1(X1, e1) = P2(X2, e2) = {9, 3} …………………. i P1{(X1-e1, X2-e2} = {9-6, 1-3)} ………………… ii Therefore, equations (i) and (ii) are gross and net demands for agent A respectively. Also, UB = X12 X42, e (3, 6) {X1, e2} = {9, 6} ……………………3 {(X1-e1, X2-e2} = {9-3, 1-6} …………4. Equations 3 and 4 are gross and net demands for agent B respectively Question 6 Player B Strategy 1strategy 2 Player A Strategy 16.5, 2                                        2, 5.5 Strategy 21, 1                                  9, 3.5 When player A uses strategy 1, B can either use strategy 1 or 2 which gives him highest payoff, so, he chooses 2 with pay off of 5.5. when A uses strategy 2, then B chooses strategy 2 also. Similarly, when player B acts by choosing strategy 1, A selects from 1 and 2 with the highest payoff, so A chooses 1 (Schwardt 2015). When B chooses strategy 2, A chooses 2 (9). Therefore, the equilibrium payoffs are (9,3.5). For a mixed strategy, there is no equilibrium payoff. While A's equilibrium payoffs are (1,1) and B has no equilibrium. Extensive form. When A moves first, the equilibrium is 1 and 9 with the payoffs of (9, 3.5). And when B moves first the equilibrium is one and its at 1,1 with the payoffs of (9, 35). GROUP C Question 7 P= 190- 2Q MC=4, cost functions, CA(QA)= CB(QB) = 4 From the profit function, firm A; ΠA = PQA-CA(QA)      ={(190-2(QA+QB)}QA-4 Max ΠA= 190QA-2QA2-2QAQB-4 =0               = 190-4QA-2QB=0          QA=47.5-0.5QB……………….1 Also, ΠB = PQB-CB(QB) = {190-2(QA+QB)}QB-4 MaxΠB =190-2QA-4QB=0……………2 and Substituting equation 1 into 2 gives; 190-2(47.5-0.5QB)-4QB, 190-95-QB-4QB=0 QB=19 units And QA = 47.5-0.5(19) =38.Therefore, firm A and B produce out put equal to 38 units and 19 units respectively. The market price, from P = 190- 2(QA+QB) (Bashir 2018) P= 190-2(38+19), P=76. The market price is 78.Firms' profits. ΠA=PQA-CA(QA)  = 76*38-4, ΠA=2884. ΠB = PQB-CB(QB)= 78*19-4=1404. The firms 'profits are 2884 and 1478 for A and B respectively. i) A case where the MC changes only, there is no difference on the output, price and profits of the firms(Wolfram et al 2015). ii) mc =4 n=6 output for firm A, following the same procedure as above, QA=38*6=228 units. And also, QB=19*^=114 units. Their profits, ΠA=PQA-CA(QA)=76*228-4=224. And also, ΠB=76*114-4=8660. iii) MCA=QA, MCB=2QB, different marginal costs incurred by two firms results into different profits. QA=38 units, QB= 19 units ΠA =p QA-CAQA=76*38-1=2887 and ΠB =p QB-CBQB=76*19-2=1442. Question 8 Q=QA+QB P=360-5Q, MC=4, Cost function =4 ΠB={360-5(QA+QB)}QB-4 Max ΠB=360-5QA-10QB=0 QB=36-0.5QA…………………………….1 Also, ΠA= {360-5(QA+QB)QA-4 360-(5(36QA-0.5QA2))QA-4 max ΠA=360-360QA-7.5QA2=0 QA=48.97. QB=36-0.5(48.97) =11.5 P=360-5(11.5+48.97) =57.57. ΠA=57.57*48.97-4=2815.4 ΠB= 57,57*11.5=658.055. i) mc=8, output remains the same, ΠA=57.57*48.97-8=2811.2. And ΠB=57,57*11.5-8=654.055 ii) MCA=2, MCB=4, output remains the same. ΠA=57.57*48.97-2=2817.2. And ΠB=57.57*11.5-4=658.055. iii) ΠA=360-5(QA+QB)QA-4 max ΠA=360-5QB-10QA=0 QA=36-0.5QB. ΠB=360-5(36-0.5QB+QB)QB ΠB=360-180QB-7.5QB2 Max ΠB=180-15QB=0 QB=12 and QA=36-6=30. P=360-5(30+12) =150 ΠA=150*30-2=4498 and ΠB =150*12-4=1796. Question 9. The market prices with complete symmetric information, means both parties are aware of the information taking place. That is to say; 200*2000=$400,000 for low quality cars and 200*4000=$800,000 for high quality cars. The sellers are better off since buyers already the prices (Campbell 2009). This means, 1000*200=$200,000 and 3750*200=750,000. Therefore, ((400000+800000) -(750000+200000)) =$250000 as the welfare gained by the sellers. In case where quality information is zero, the seller is willing to accept $1000 for low cars and $3750 for high cars (Dada 2015). Then, -$250000 is the lost gain by the sellers. Only 19 cars of high quality are available. With zero quality information for buyers, no welfare gained and prices are constant for which the buyer is willing to pay (Gaprindashvili 2018). And finally, sellers with complete quality information and buyers with zero, there is over exploitation of consumer surplus by the sellers (Bashir 2018). Question 10 Social optimal level equates the MC to MB From; MEC=MCA, 19-4E=2E E=3.2 the social optimal level is 3.2. Min 19-4E=0=4 as the abatement cost and Min 2E=2 as external cost. P=0.9, the deadweight loss= 2*0.9=1.8 as the deadweight loss. Deadweight loss= (19-4*2) *1.1=12.1 References Chin Yung Wei, Thenmoley.R, Elhag Siddig and David Asirvatham.2018. E-Commerce Adoption and Analysis of the Popular E-commerce Business Sites in Malaysia. Graduate School of Management, Management and Science University, Malaysia. Vol 9(2):347. Retrieved from: https://www.omicsonline.org/open-access/ecommerce-adoption-and-analysis-of-the-popular-ecommerce-business-sites-in-malaysia-2151-6219-1000347-100905.html Muhammad  Bashir.2018. A Class of Multi-Attribute Auction Transformed into Single- Attribute Auction on Margin Bid. Business and Economics Journal. Business Administration, Central South University, Changsha, Hunan, China. Vol 9(2):352. Retrieved from: https://www.omicsonline.org/open-access/a-class-of-multiattribute-auction-transformed-into-singleattribute-auction-on-margin-bid-2151-6219-1000352-102232.html Kyle Shobe.2018. Productivity Driven by job Satisfaction, Physical Work Environment, Management Support and Job Autonomy. Business and Economics Journal. Department of Finance and General Business, Missouri State University, USA. Vol 9(2): 351. Retrieved from: https://www.omicsonline.org/open-access/productivity-driven-by-job-satisfaction-physical-work-environment-management-support-and-job-autonomy-2151-6219-1000351-102231.html Saqib Amin.2018. Does the Entrepreneurial Human Capital is Important for Organizational Performance? Business and Economics Journal. Department of Economics, University of Lahore, Lahore, Pakistan. Vol 9(2): 350. Retrieved from: https://www.omicsonline.org/open-access/does-the-entrepreneurial-human-capital-is-important-for-organizational-performance-2151-6219-1000350-102230.html Fabricio Stocker.2018. Institutional Environment and Internationalization: The Case of Brazilian Agency. Business and Economics. School of Economics, Business and Accounting, University of Sao Paulo, Brazil. Vol 9(2): 349. Retrieved from: https://www.omicsonline.org/open-access/institutional-environment-and-internationalization-the-case-of-brazilian-agency-100907.html Balal Karimi, Mostafa Davtalab and Ali Abdali.2018. A Suitable Business Model for Bank Branches: Combining Business Model and Malmquist Productivity Index (MPI). Business and Economics Journal. Department of Mathematics, Karaj Branch, Islamic Azad university, Karaj, Iran. Vol 9(2). Retrieved from: https://www.omicsonline.org/open-access/a-suitable-business-model-for-bank-branches-combining-business-model-and-malmquist-productivity-index-mpi-2151-6219-1000348-100906.html Mathew Dada. 2015. Theoretical Analysis of Microeconomic Effect of Public Investment. Asian Journal of Economic Modelling. Department of Economics, Wellspring University, Benin city, Nigeria. Vol 3(1): 1-7. Retrieved from: https://www.aessweb.com/pdf-files/60-ajem-2015-3(1)-1-7.pdf Wolfram Elsner, Torsten Heinrich, and Henning Schwardt.2015. The microeconomics of Complex Economies: Evolutionary, Institutional, Neoclassical and Complexity Perspectives. UK, Academic Press. Issues, 49:1, 297-299. Retrieved from: https://www.uni-marburg.de/fb19/fachgebiete/wirtschaftsgeographie/mitarbeiterinnen_ordner/vonproffs/book_review_v_proff.pdf Nathan W and Kenneth Gillingham. 2015. The Microeconomic theory of the Rebound Effect and its Welfare Implications. Journal of the Association of Environment and Resource Economics. Yale University. Retrieved from: https://environment.yale.edu/gillingham/ChanGillingham_ReboundTheory.pdf Ola Olsson. 2015. A Microeconomic Analysis of Institutions. Department of Economics, Goteborg University. Retrieved from: https://ecsocman.hse.ru/data/086/784/1216/gunwpe0025.pdf Giorgi Gaprindashvili. 2018. Main Challenges for Georgia's Social-Economic policy. Journal of Global Economics. Tbilisi State University, Tbilisi, Georgia. Vol 6(2). Retrieved from: https://www.omicsonline.org/open-access/main-challenges-for-georgias-socialeconomic-policy-2375-4389-1000290-102237.html Raffia Bashir. 2018. Sectarianism: Economic Impact on Subcontinent. Journal of Global Economics. Institute of Social Sciences, Bahauddin Zakariya University, Multan, Pakistan. Vol 6(2): 292. Retrieved from:  https://www.omicsonline.org/open-access/sectarianism-economic-impact-on-subcontinent-18751947-2375-4389-1000292-102233.html Mankiw, N. 2014. Principles of Microeconomics. Cengage Learning. p. 32. ISBN 978-1-305-15605-0. McConnell, Campbell. 2009. Economics. Principles, Problems and Policies. 18th ed. New York: McGraw-Hill. ISBN 9780073375694. Archived from the original (PDF contains full textbook) on 6 October 2016. Free Membership to World's Largest Sample Bank To View this & another 50000+ free samples. Please put your valid email id. E-mail Yes, alert me for offers and important updates Submit  Download Sample Now Earn back the money you have spent on the downloaded sample by uploading a unique assignment/study material/research material you have. After we assess the authenticity of the uploaded content, you will get 100% money back in your wallet within 7 days. 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