Consumerand Cost Analysis Problems
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Consumerand cost analysis problems
Consumer demandanalysis and estimation applied problems
Problem 1
Gneiting &Ranjan (2011) assert that during the analysis of consumer demand andestimation of the probability of performance for a commerce, it isalways supportive to utilize a weighted scoring approach for theanticipated attributes. A weighted scoring approach is amultiattribute approach, which involves documentation of allnonfiscal aspects pertinent to a project and then allocates weightsto each of the aspects to reflect their comparative significance.
a. As per theprovided analysis above, if Patricia decides to open a restaurant insuburban LA, then taste is three times and two times as significantas location and price respectively. As such, suing the weightedscoring approach, then the weights of the three aspects appear as
T = 3L T = 2P,which means that if T is 1, then L is 1/3 and P is 1/2
Then, theexpected utility (EU) for steak if Patricia opened the restaurant insuburban LA is
80 + 1/3 * 55 + ½* 65 considering T = 3L and 2P = 130.8333
The EU for pizzain suburban LA is 70 + 1/3 *80 + ½ * 50 = 121.666667
Based on thetotal EU, Patricia should open a Steak restaurant as it has thehighest EU of 130.83 compared to the EU of pizza of 121.67. Opening asteak restaurant will give Patricia an EU of 9.167 more than, if shechose to open a pizza restaurant.
On the otherhand, location is three times and two times as significant as tasteand price if Patricia opens a restaurant in the Metropolitan area
I.e. L = 3T and L= 2P thus, the EU for steak is 55 + 1/3 * 80 +1/2 *65 = 114.167 andthe EU for pizza is 80 + 1/3 * 70 + ½ * 50 = 128.33. This givesPatricia a difference of 14.167 by opening a pizza restaurant. Inthis regards, Patricia should open a steak restaurant in suburbanarea and a pizza restaurant in the Metropolitan area.
b. If Patriciachoses the Metropolitan area, she should open a pizza restaurant asit has the highest EU of 128.33 compared to an EU of 114.167 forsteak in the same area, a difference of an EU of 14.167. I.e. EU forsteak is 55 + 1/3 * 80 +1/2 *65 = 114.167 and the EU for pizza is 80+ 1/3 * 70 + ½ * 50 = 128.33
c. With theprobability of finding a restaurant in the suburban area as 0.7 andthat of the Metropolitan area as 0.3, the EU for steak and pizzarespectively in the suburban area would be 130.83 / (1 + 0.07) =122.27 and 121.67 / (1 + 0.07) = 113.71. As such, Patricia wouldstill choose a steak restaurant as it would have an EU of 122.27, anEU of 8.57 more than pizza. On the other hand, the EU for steak andpizza for the metropolitan area would be 114.167 / (1 + 0.03) =110.84 and 128.33 / (1 + 0.03) = 124.60 thus, the pizza businesswould still be the best option for Patricia.
d. One can see anillustration of an alternative based on weighing numerous underlyingattributes when picking a supplier from a collection of two providersbased on the weighted score using such aspects as magnitudes ofsuperiority, cost effectiveness, industrial capability and servicelevel. In this regards, a weighted average score results in aninclusive assessment of choices by bearing in mind all thesignificant factors as well as the provision of multiple changes in asimple and timely manner. However, individuals can influence theweights allocated to highlight the significance of attributes. Infact, Png (2013) asserts that administrators can sway the purchasingperformance of consumers by altering one or more attributes in theconsumers’ decision process. In addition, the approach can resultin a biased valuation due to the lack of scientific technique. As Png(2013) suggests, Patricia choice to open a restaurant in either thesuburban or the metropolitan area must take into consideration theuncontrollable attributes including changes in competitive behaviorand consumer incomes.
Problem 2
a.
Original 
Variable 
New 

Qx 


Px 

0.95 
– 51.3 
Py 
45 
0.64 
28.8 
Ax 
0.62 
120 
74.40 
Hence, Qx = – 14– 54 * 0.95 + 45 * 64 + 0.62 * 120 = 37.9
a. Png (2013) andPage (2013) define price elasticity of demand as the proportionvariation in quantity required followed by the proportion variationin price represented by E(p) = ∂Q∂P * PQ thus, ∂Q∂Px = 54.Based on Png (2013) and Page (2013) definition, the price elasticityis – 1.35 i.e. – 54 (0.95 / 37.9), meaning demand will declineby 1.35% for each 1% rise in price and vice versa.
b. Page (2013) and Feldstein (2011) denote inverse demand curve as autility or function that plots the amount of production demanded tothe dependent variable i.e. market price, where the function is Px =f(Qx) in the above problem. The demand function is Px = (14 + 45Py +0.62Ax – Qx)/54, which means that the inverse demand curve (Px) =1/54 * (89.2 – Ox)
c. Given that thecost of manufacturing a donut is pegged at $0.15 and the analysis hasprovided a price elasticity of 1.35, diminishing the price by 1%means that the demand will increase by 1.35%. In this regards,Newton’s donuts can reduce price to increase demand and ultimatelymaximize profit bearing in mind that price elasticity will ensurethat price will not decrease further.
d. Going by thedemand function increasing advertising expenses by US$1 increasesdemand by 0.62 * 1 = 0.62, but the rise in profit from the improveddemand i.e. 0.62 * (0.95 – 0.15) = $0.496 is lower than the cost ofthe increased advertising hence, Newton should not escalatemarketing expenditures.
Production costanalysis
Problem 1
a.
Workers (V) 
Qty of Pizzas 
No. of Pizza (TP) 
Marginal product (AP = TP/V 
Change in MP ( = TP/V 
No of Pizzas/ Employee cost (MC) 
0 
0 
0 
0 
0 
0 
1 
75 
75 
75 
500 
6.67 
2 
180 
90 
30 
1000 
5.56 
3 
360 
120 
75 
1500 
4.17 
4 
600 
150 
60 
2000 
3.33 
5 
900 
180 
60 
2500 
2.78 
6 
1140 
190 
60 
3000 
2.63 
7 
1260 
180 
120 
3500 
2.78 
8 
1360 
170 
20 
4000 
2.94 
The law ofvariable proportions according to Garleanu & Pedersen (2011),demonstrates that the aggregate output will likely increase at anincreasing rate in the beginning but ultimately increase at adiminished rate as one adds more attributes to the fixed inputs.Lowe, Papageorgiou, & Sebastian (2012) describe marginal productas a change in aggregate product for a onecomponent variation in theattribute inputs i.e. ΔTP/ΔV. In this regards, based on the tableabove and bearing in mind that MP is adjustable or increasingreturns it increases rapidly from 1 to 3, becomes constant at 4 and5, then starts to decrease from 6.
b. 6 employeesappear as efficient since they produce the highest number of pizzasat 190
c. Lowe et al(2012) define marginal cost as the change in aggregate cost arisingfrom manufacturing one additional piece. Based on the table above,the marginal cost is curtailed at 6 employees since at this stage, MCis at 2.63 for every pizza.
d. Marginalproductivity decreases when one hires more employees in the short runafter a specific level since there will be at least one static factorof production, such as capital. For example, with some fixed factorsof production workers will congest and share the fixed factors, whichcause the MP of labor to reduce as increased number of employeesshare the same capital or fixed factors of production as before.
e. Garleanu &Pedersen (2011) assert that businesses tent to build connections overtime thus, expanding a business influence the economies of scalesince it helps lower costs. However, at a certain level, Williamwould fail to lower costs due to the diminishing returns of MP, forexample, the total number of pizza is highest at 8 employees but sois the cost of production. However, at 6 employees, the businessenjoys efficiency thus, the business has a constant returns to scaleat 6 employees and diseconomies at 8 employees.
Problem 2
a. As suggestedabove, Lowe et al (2012) define marginal cost as the change inaggregate cost arising from manufacturing one additional piece i.e.ΔTVC/ΔQ therefore, MC = 31450 – 38970 = 7520 / (1000 – 1200)= 37.6
b. Total variablecost or TVC = 3450 + 20Q + 0.008Q^{2} = 3450 + 20 * 1000 +0.008 * 1000^{2} = 31450 hence, when Q is 1000 Totalvariable cost is 31450, which puts an enlarged variable cost at 7250plus the extra 2000 required for the lease.
c. Young &Makhija (2014) and Kamien & Schwartz (2012) assert that firmsmaximizes profit when MC = MR, which means that the firm wouldmaximize profit when MC and MR are at 104 thus, profit maximizationwould appear at production level 1500.
d. Paradise Shoesshould expand beyond 1200 shoes per week since their optimum level isbeyond 1200 shoes. As suggested TVC is 31450 at Q = 1000. However,increasing production to 1200 shoes a week will require the companyto lease a machine for $2000, but based on profit maximization andthe level of MC and MR, the level will not provide the mostefficiency thus, the company should go beyond 1200 shoes.
.
References
Feldstein, P. (2011). Health care economics. CengageLearning.
Garleanu, N., & Pedersen, L. H. (2011). Marginbased assetpricing and deviations from the law of one price. Review ofFinancial Studies, hhr027.
Gneiting, T., & Ranjan, R. (2011). Comparing density forecastsusing thresholdand quantileweighted scoring rules. Journalof Business & Economic Statistics, 29(3).
Kamien, M. I., & Schwartz, N. L. (2012). Dynamicoptimization: the calculus of variations and optimal control ineconomics and management. Courier Dover Publications.
Lowe, M., Papageorgiou, C., & Sebastian, F. P. (2012). The Publicand Private Marginal Product of Capital.
Page, T. (2013). Conservation and economic efficiency: anapproach to materials policy. Routledge.
Png, I. (2013). Managerial economics. Routledge.
Young, S. L., & Makhija, M. V. (2014). Firms` corporate socialresponsibility behavior: An integration of institutional and profitmaximization approaches.Journal of International BusinessStudies, 45(6), 670698.