MPH 511: ECONOMIC ANALYSIS FOR BUSINESS MPH 511: ECONOMIC ANALYSIS FOR BUSINESS ASSIGNMENT ONE ASSIGNMENT ONE SUBMITTED TO: Prof. Rajendra Prasad Shrestha, Ph.D Master of Philosophy in Management Faculty of Management Tribhuvan University Submitted by: Nischal Thapa Roll No 14/012 MPhil in Management, TU
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MPH 511: ECONOMIC ANALYSIS FORMPH 511: ECONOMIC ANALYSIS FOR BUSINESSBUSINESS
ASSIGNMENT ONEASSIGNMENT ONE
SUBMITTED TO:Prof. Rajendra Prasad Shrestha, Ph.D
Master of Philosophy in ManagementFaculty of Management
Tribhuvan University
Submitted by:
Nischal ThapaRoll No 14/012
MPhil in Management, TU
2
April, 2013
PROBLEM 1Suppose, A B C Book Seller located at the university complex is selling Econometric Book. The cost per book of the seller (including transport and other related costs) is 76. The firm has other overhead and marketing cost which is considered to be fixed cost. The marginal cost is 76 assuming it is constant. There is another book seller located in the same complex. So, the manager of ABC Book Seller estimates very high price elasticity of demand for econometric books. The estimated price elasticity of book is 2.5. Therefore, the manager of ABC Book Seller decided to put 67% mark-up on the cost per book. Do you think the price decided by the manager is optimal?
ANSWER 1Given in the question, Cost per book (including transport and other related cost) = Rs. 76Marginal Cost (MC) = Rs. 76
Estimated price elasticity of book (ep) = - 2.5
Mark-up = 67% of costs per bookPrice per book (P) = Cost per book (1+ Mark-up) = Rs. 76(1 + 0.67) = Rs. 126.92Here, According to Arc elasticity demand Marginal Revenue (MR) = P (1 – )Or, 76 = P (1– )Or, P = 76/0.6 P = 126.67 P = Rs. 127 (roundoff)Conclusions: Even though in the absolute figures, the price might not be absolutely optimal, but in roundoff figure, the price is optimal.
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PROBLEM 2An American company provides fertilizers and weed control lawn services to residential customers of Lagankhel. Its seasonal service package, regularly priced at $250, includes several chemical spray treatments. As part of an effort to expand its customer’s base, American company offered $50 off its regular price to customers in the Lagankhel area. Response was enthusiastic, with sales rising to 5750 units (Package) from the 3250 units sold in the same period last year.
a) Calculate the arc price elasticity of demand for American company service.b) Assume the arc price elasticity (from part A) is the best available estimates
of the point price elasticity of demand. If marginal cost is $ 135 per unit for labour and materials. Calculate company’s optional markup on price and its optimal price.
ANSWER 2Given in the question,Price of each service package (P1) = $ 250Change in Price ( P) = $ 50Price of new service package (P2) = 250–50 = $ 200Quantity demand before new service package (Q1) = 3250 unitsQuantity demand after new service package (Q2) = 5750 unitsChange in Quantity demand ( Q) = 2500 unitsNow, Calculation of Arc Price Elasticity (ep);
We know that, ep = ×
Or, ep = × = = 2.5Arc Price Elasticity (ep)= 2.5
Now, calculation the optimal price and markupHere, Marginal cost (MC) = $135We know that, at the level of optimal profit, MC is equal to MR
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MR = MC = $ 135Again,We know that, MR = P (1– )Or, 135 = P (1– )Optimal price (P) = $ 225Therefore, Price per book (P) = Cost per book (1+ Mark-up)or $225 = MC (1+Mark-up%)or, $ 225 = $ 135(1 + Mark-up%)Mark up percentage = – 1Mark up percentage = 66.67%Conclusion:Hence, the company’s optimal price is $ 225 and its optimal markup is 66.67%.
PROBLEM 3
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ABC Company is operating for the last 10 years in Kathmandu Valley. The company wanted to hire you as a consultant to determine profit maximizing output and price. From the ten years data on the sales and price supplied by the Accountant of the company you run regression program and came with the following demand and cost functions P=90-Q and a cost function as C=10+0.5Q2 . The General Manager of the company told you that the company was producing 160 units as an optimal quantity of production. How do you suggest the General Manager of the company?
ANSWER 3Given in the question,Demand function; P = 90–2Q Cost function; C = 10+0.5 Q2
General Manager's assumption of optimal quantity of production (Q) = 120 unitHere;Total Revenue (TR) = P × Q
Again, we know that, Profit (П) = TR – TC П = (90Q –2Q2) – (10+0.5 Q2) Profit Function; П= –2.5Q2 +90Q –10 Now, MR = == 90– 4Qand, MC = == 0+1Q = QAccording to the profit maximization principle,MC = MROr, Q = 90 – 4QOptimal quantity (Q) = 18 unitsTesting of reliability of above calculation:Condition 1: At the profit maximization level of output; Marginal profit or 1st order derivative of profit must be equal with zero, Taking 1st order derivative of profit, Marginal Profit = = = –5Q+90
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Then, substituting the value of Q = 18,
Marginal profit = = –5 ×18 + 90 = 0 = 0Condition 2: Again, at the profit maximization level of output; 2nd order of derivative of profit must be less than zero (i.e. negative), Taking 2nd order derivative of profit, < 0Or, = – < 0Or, = – < 0Or, = – < 0Or, = –4 – 1 < 0Or, = –5 < 0Thus, the first derivative or marginal profit is zero and 2nd order derivative of the firm is found less than zero (i.e. – 5). Hence, the optimal quantity of production that has profit maximization is 18 units.
Conclusion: At ABC Company, since the General Manager's assumption of optimal quantity of production (i.e. 120 units) is not equal to the calculated optimal quantity (i.e. 18 units); hence, the assumption of optimal quantity of production is wrong. Therefore the general manager should produce 18 units as an optimal quantity of production for profit maximization.
PROBLEM 4A M.Phil Graduate wanted to started a business. He estimated cost and revenue of the business. Suppose his cost ( C ) and Revenue( R ) functions are given as C= 100 + 5 Q2 and R = 150 Q – 2.5 Q2 . find:
a) Profit maximizing output and price/output combinationb) Maximum profitc) Optimal price/output combination if marginal cost of production is 10Q.
ANSWER 4
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Given in the question, Cost function; C = 100 + 5 Q2
Marginal Revenue (MR) = = 150– 5Q Marginal Cost (MC) = = =0+10Q = 10QAccording to profit maximization principle, Marginal revenue must be equal to Marginal cost.Therefore, MC = MR
10Q = 150 – 5QOptimal quantity (Q) = 10 units
Condition 1:At profit maximizing level of output; Marginal profit or 1st order derivative of profit must be equal with zero, Taking 1st order derivative of profit,
Marginal Profit (MP) = = = –15Q+150Substituting the value of Q (= 10) then we get,
= –15 × 10 + 150
= 0
Condition 2:Again, at profit maximizing level of output; 2nd order of derivative of profit must be less than zero (i.e. negative), Taking 2nd order derivative of profit,
< 0
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Or, = <0Or, = < 0Or, = –15< 0Thus, the first derivative or marginal profit and 2nd order derivatives of the firm are found zero and < 0 i.e. – 15 respectively. Therefore, the profit maximizing optimal quantity of production is 10 units.
Now, substituting the value of Q (= 10 units) in price function, revenue function and cost function, we get P = 150 – 2.5 ×10Optimal price (P) = Rs. 125Now, Total Revenue (TR) = P × Q = Rs. 125 ×10 = Rs. 1250 Total Cost (TC) = 100 + 5 × 10 2 =Rs.600
Now, Maximum profit = TR –TC Maximum profit = Rs.1250 –Rs. 600 = Rs. 650Conclusion: Therefore, the maximum profit that can be earned is Rs. 650 by producing 10 units of output.
PROBLEM 5 With the launching of M.Phil Program of Faculty of Management, a term of graduate students wanted to start a Book Stall close to M.Phil building. There are only 25 students in the M.Phil Program. The estimated demand of book at different levels of price is given below:
Books (in No.)
5 10 15 17 18 20
Price (Rs.) 1500 1200 1000 800 500 400The cost function is assumed to be TC= C = 100 + 5 Q2. Suppose the Book Stall is only selling the books related to Economic Analysis for Business. At what level of
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book sale the Book Stall maximizes its profit and what is the price output combination to the Stall. (Note: Formulas for obtaining the value α(constant) and β (coefficient) are
β =
respectively or it can be solved by using two simultaneous equations as ∑Yi = nα + β ∑Xi and ∑Xi ∑ Yi = α ∑Xi + β (∑Xi)2
What will happen if cost function Changed to TC = 100 + 10 Q2. ANSWER 5
= 13 unit (approximately )Testing of reliability of above calculation:Condition 1At profit maximizing level of output; Marginal profit or 1st order derivative of profit must be equal with zero, Taking 1st order derivative of profit, Marginal Profit = = =1917 – 153.55QSubstituting the value of Q = 12.48 then we get,
= 1917 – 153.55 × 12.48 = 0
Condition 2:Again, at profit maximizing level of output; 2nd order of derivative of profit must be less than zero (i.e. negative), Taking 2nd order derivative of profit, Or, = – Or, = –143.55 – 10 Or, = –153.55 < 0Thus, the first order derivative or marginal profit and 2nd order derivatives of the firm are found zero and < 0 (i.e. – 153) respectively. Hence, the profit maximizing optimal quantity of production is 13 units.Now substituting the value of Q (=12.48) in price, revenue and costs and profit function, we getP = 1917 – 71.77 × 10Optimal price (P) = Rs. 1200Total Revenue (TR) = P × Q = 12.48 × 1200 =Rs. 14976Total cost (TC) = 100 + 5Q2 = 100 + 5 × (12.48) 2 = Rs. 878.75
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Total profit (П) = TR –TC = Rs. 14976 – Rs. 878.75 = Rs. 14097.25 Conclusion: Here profit can be maximized up to Rs. 14097.25 by producing 13 units of output.
PROBLEM 6Let the demand facing a firm for its product be expressed by the following functions Q = 25 - 0.5 P (Where Q = quantity and P = Price), and cost function as C = 25 – 2 Q + 4 Q2. Compute (a) profit maximizing output, (b) Justify profit maximizing output.
ANSWER 6Given in the question, Demand function; Q = 25–0.5 POr, Demand function; P = 50 – 2QCost function; C = 25 – 2Q + 4Q2
Revenue function; R = P × Q = (50 – 2Q) × Q = 50Q – 2Q2
According to profit maximization principle, Marginal revenue must be equal to Marginal cost.Therefore, MC = MROr, –2 +8Q = 50 –4Q Q = unit = 4.33 units = 5 units (aprox)Testing of reliability of above calculation:Condition 1:At profit maximizing level of output; Marginal profit or 1st order derivative of profit must be equal with zero, Taking 1st order derivative of profit,
MP = = = 52 – 12 Q
If Q = then,
= 52 – 12 × = 0
Condition 2:At profit maximizing level of output; 2nd order of derivative of profit must be less than zero, Taking 2nd order derivative of profit, Or, = – Or, = – Or, = –4 – 8 Or, = –12 < 0Conclusion: The first order derivative or marginal profit and 2nd order derivatives of profit are found zero and < 0 i.e. – 12 respectively. Hence, the profit maximizing optimal quantity of production is 13/3 units.
Now substituting the value of Q (=13/3) in Profit function, we getOptimal profit, П = 52Q – 6Q2 – 25Or, П = 52 × – 6 × × –25П = Rs. 87.66Under the given condition, optimal profit is Rs. 87.66.
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PROBLEM 7A manufacturing company is operating in Kathmandu valley with the demand function given as P = 40 – Q, and total cost function as C = Q2 + 8 Q + 2. If the company wanted to maximize profit what is the price combination and the total profit and revenue? The management of the company realizes the need for capturing market. Therefore, it started to promote its product with the strategy of sales revenue maximization instead of profit maximization. What will be the price output combination and total profit under the condition of sales revenue maximization? The shareholders of the company did not like market share capture strategy (sales revenue maximization) followed by the management. The shareholders shoed strong dissatisfaction against the management in its Annual General Meeting (AGM). They argued that management should not be given opportunities for free play in the company. The shareholder’ meeting consensually decided to put restriction with minimum profit of Rs. 10. Under this condition, what is the optimum price (P) output (Q) combination and total revenue?
ANSWER 7Given in the question,Demand function; P = 40 – Q
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Cost function; C = Q2 +8Q +2Revenue Function; R = P × Q = (40 – Q ) × Q = 40Q – Q2
П = TR – TC Or, П = 40Q – Q2 – (Q2 + 8Q + 2) П = 32 Q – 2Q2 – 8Case 01: Profit maximizationAccording to profit maximization principle, Marginal revenue must be equal to Marginal cost.Therefore, MC = MR 40 – 2Q = 2Q + 8
Q = 8 unitsCondition 1: At profit maximizing level of output; Marginal profit or 1st order derivative of profit must be equal to zero, Taking 1st order derivative of profit,
Marginal Profit (MP) = = =32 – 4Q
If Q = 8 unit, then,
= 32 – 4 × 8= 0
Condition 2:At profit maximizing level of output; 2nd order of derivative of profit must be less than zero (i.e. negative), Taking 2nd order derivative of profit, = – = – = –2 – 8 = –10 < 0Conclusion: The first order derivative or marginal profit and 2nd order derivatives of the profit are found zero and < 0 i.e. – 10 respectively. Hence, the profit maximizing optimal quantity
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of production is 8 units. Now, substituting the value of Q (= 8 units) in Price Function, Revenue Function, Cost function and Profit Function, we get P = 40–8 Optimal price (P) = Rs. 32Total Revenue (TR) = P × Q = Rs. 32 × 8 = Rs. 256 Total Cost (TC) = Q2 + 8Q + 2TC = 82 +8x8 +2Total Cost = Rs. 130And, Optimal profit = TR –TC Optimal profit = Rs.256 –Rs. 130 = Rs. 126.00
PROBLEM 8A company developed be a group of M. Phil Graduates is facing with following demand and cost functions: P = 50 - 0.5Q (Demand function) C = 1.5 Q2 +5 Q + 10 (Cost function), where, Q = quantity in thousands of unit, and P = Price in Rupees, C = Total cost. The graduates wanted to set the objective of the company. Therefore, they conducted a brainstorming session. In the session, certain group of graduates put forwarded profit maximization as an objective of the company while other group argued in favour of revenue maximization as objective of the company. Similarly, agroup of graduates wanted to have revenue maximization with a minimum profit of Rs. 20. In this situation, they wanted to use their knowledge gained from the course entiled “Economic Analysis for Business”. What is the process they will use for determining price output combination and what is the price output combination including total profit and revenue based on the above demand and cost functions under different conditions?
ANSWER 8Given in the question, Demand function; P = 50 – 0.50 QCost Function; C = 1.5 Q2 + 5Q + 10Revenue Function; R = P × Q = 50Q – 0.50Q2
Total Profit (П) = TR – TCOr, П = – 2Q2 + 45 Q – 10Minimum Profit = Rs.20Marginal Revenue (MR) = = = 50 – QMarginal Revenue (MC) = = = 3 Q + 5Case 01: Profit maximizationAccording to profit maximization principle, Marginal revenue must be equal to Marginal cost.Therefore, MC = MR
MR– MC = 0
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Or, 50 – Q – (3 Q +5) = 0 Q = 11.25 unitCondition 1: At profit maximizing level of output; Marginal profit or 1st order derivative of profit must be equal to zero, Taking 1st order derivative of profit,
Marginal Profit = = = 45 – 4Q
If Q = 11.25 then,
= 45 – 4 × 11.25 = 0
Condition 2:At profit maximizing level of output; 2nd order of derivative of profit must be less than zero (i.e. negative), Taking 2nd order derivative of profit,
= 45 – 4Q
= = - 4 >0Conclusion: The first order derivative or marginal profit and 2nd order derivatives of the firm are found zero and < 0 i.e. – 4 respectively. Hence, the profit maximizing optimal quantity of production is 11.25 units.
Now, substituting the value of Q (= 11.25 units) in Price Function, Revenue Function Cost function and Profit Function, we get Price (P) = 50 – 0.50 Q = 50 – 0.50 × 11.25 =Rs. 44.37Total revenue (TR) = 50 Q – 0.50 Q2
From the above computation, the 1st case of profit maximization has an optimum output of 11.25 units and optimal price of Rs.44.37 that generate the total revenue, total cost and profit of Rs. 499.22, Rs. 256.09 and Rs. 243.13 respectively. The 2nd condition of sales revenue maximization has an optimal output of 50 units and optimal price of Rs. 25 that generate the Total Revenue and Total Cost are Rs. 1250 and Rs. 4010 respectively. But there is loss of Rs.2760.The 3rd condition of sales revenue maximization with constraint of profit of Rs.20, the optimum output is 21.81 units and optimal price is Rs. 39.09 that should generate the total revenue and the total cost at the level of output are Rs.852.63 and Rs.832.56 respectively.
As, the profit maximization condition generates highest profit with lowest sales, the best approach is profit maximization approach.
PROBLEM 9
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A group of students started a business with a view to create employment for themselves. Their demand and cost functions of their product are as follows: P = 75 – 1.5 Q (Demand function) C = 3Q2 + 15 Q + 30 (Cost function)Where, Q = quantity in thousand of unit, and P = Price in Rupees, C = Total cost. Find the price, total revenue, total cost and total profit of the group under the objective of:
(a)Profit maximization, (b)Sales revenue maximization, and (c) Sales revenue maximization with a minimum profit of Rs. 30.
ANSWER 9Given in the question,Demand function; P = 75 – 1.50 QCost Function; C = 3 Q2 + 15Q + 30Revenue Function; R = P x Q = 75Q -1.50Q2
MR– MC = 0Or, 75 – 3Q – (6 Q +15) = 0 Optimal output (Q) = 6.67 unitCondition 1: At profit maximizing level of output; Marginal profit or 1st order derivative of profit must be equal to zero, Taking 1st order derivative of profit,
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Marginal Profit = = = – 9 Q +60
If Q = 6.67 then,
= –9 x 6.67 + 60= 0
Condition 2:At profit maximizing level of output; 2nd order of derivative of profit must be less than zero (i.e. negative), Taking 2nd order derivative of profit,
Or, = – 9 Q +60
Or, = = - 9
Conclusion: The first order derivative or marginal profit and 2nd order derivatives of the profit are found zero and < 0 i.e. – 9 respectively. Hence, the profit maximizing optimal quantity of production is 6.67 units.
Now, substituting the value of Q (= 6.67 units) in Price function, Revenue function and Cost function, we get
From the above computation, at the level of the profit maximization, the firm has an optimum output is 6.67 units and optimal price is Rs.65 that should generate the total revenue, total cost and amount of profit are Rs. 433.52, Rs. 263.52 and Rs. 170.00 respectively.
Case 02: Sales maximizationAccording principle of sales revenue maximization; Marginal Revenue (MR) = 0MR = 75 – 3Q = 0Output (Q) = 25 units
Price (P) = 75 – 1.5 × 25 =37.5
Total revenue (TR) = P × QTR = 37.5 × 25TR = Rs.937.50
At the level of sales revenue maximization, the firm has an optimal output of 25 units and optimal price of Rs. 37.5 that generate the total revenue and total cost of Rs. 937.50 and Rs. 2280 respectively. But there is loss of Rs.1342.50.
Case 03: Sales maximization with constraint of profit amount of Rs. 30At minimum level of profit of Rs.30; Total Profit (П) = TR – TC = Rs. 30Or, - 4.5Q2 + 60 Q – 30 = 30Or, - 4.5Q2 + 60 Q – 60 = 0Or, 0.3Q2 – 4 Q + 4 = 0Using quadric equation formula,a = 0.3, b = – 4 and c = 4Or, Q = Nischal Thapa, MPhil-TU
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Or, Q = Or, Q = Taking positive sign, Or, Q = Or, Q = 12.25 unitsTaking negative sign, Or, Q = Or, Q = 1.08 units Hence, the required quantity of output is 12.25 units
Conclusion: At the level of sales revenue maximization with profit constraint of Rs.20, the firm has the optimum output of 12.25 units and optimal price is Rs. 56.63 that generate the Total Revenue and the Total Cost are Rs.693.66 and Rs.663.94 respectively.
PROBLEM 10The past records of price and sales of shirt at different points of time are as follows:
From the above records of prices and sales of shirts, calculate profit maximizing number of shirt and price including total revenue and profit, given the cost function of C = 3Q2 + 15 Q + 30. What will happen in quantity demand when price increased at Rs. 180 and elasticity of demand? Estimate new function relationship and its price output combination? Interpret your results.
Again, MC = = 6Q +15П = TR – TC П = (183.48 Q –1.3043Q2) – (3Q2 +15Q +30) П = – 4.3043 Q2 + 168.48Q – 30 According to profit maximization principle, Marginal revenue must be equal to Marginal cost.Therefore, MC = MR6Q +15 = 183.48– 2.6086 Q8.6086 Q = 168.48Optimal quantity (Q) = 19.57 units = 20 units (approx)
Condition 1: At profit maximizing level of output; Marginal profit or 1st order derivative of profit must be equal to zero, Taking 1st order derivative of profit,
Marginal Profit = = = – 8.6086 Q + 168.48
If Q = 19.57 then,
= – 8.6086 x 19.57+168.48 = 0
Condition 2:At profit maximizing level of output; 2nd order of derivative of profit must be less than zero (i.e. negative), Taking 2nd order derivative of profit, 2nd order derivative, < 0
= – 8.6086 Q + 168.48
= = – 8.6086
Thus, the first order derivative or marginal profit and 2nd order derivatives of the firm are found zero and < 0 i.e. – 8.6086 respectively. Hence, the profit maximizing optimal quantity of production is 19.57 units.Now, substituting the value of Q (= 19.57 units) in Price function, Revenue function and Cost function, we get
Explanation: At the profit maximizing objective, the firm's optimum output is 19.57 units and optimal price is Rs. 157.95 that generates the total revenue, the total cost and optimal profit of Rs.3091.08, Rs.1472.50 and 1618.58 respectively.
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A Case of Wry Island[I] Initial Equilibrium Initial Equilibrium (for 9 workers from Farm A, B and C)Table 1.1Total Physical Product (TPP), Marginal Physical Product (MPP), Marginal Revenue Product (MPR) of
10 2050 75 $ 300 3475 150 $ 600 2375 125 $ 500Table 1.2Allocation of Resources and Distribution of Income
Units ComputationRye only @ $4 per bu. 9
workerWages rate $ $ 1,300Farm A:
Workers No. 2Rent $ 725×$4 – 2×$1300 $ 300
Farm B:Workers No. 5Rent $ 2450×$4 –
5×$1300$ 3,300
Farm C:Workers No. 2Rent $ 675×$4 – 2×$1300 $ 100
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Farm D:Workers No. –Rent @ $ –
Total wages bill (A + B + C + D)
9 × $ 1300 $ 11,700
Total rent $ 300 + $ 3300 + $ 100
$ 3,700
Total Farm income (wages & rent)
$ 15,400
Total value of Farm (P × Q) $ 4 × 3850 $ 15,400Conclusions:Out of 9 labourers, 2 work in Farm ‘A’, 5 work in Farm ‘B’ and 2 work in Farm ‘C’. The equilibrium wages rate of all Farms is $ 1300. The rent earned by Farm ‘A’, Farm ‘B’ and Farm ‘C’ are $ 300, $ 3,300 and $100 respectively being total of $ 3,700.[II] InflationIn case of inflation, the price of rye rises to $40 per bushel. Therefore, at the new equilibrium, MRP (= the wage rate) will be $13000. The number of laborers and rent earned on various farms are as follows:Table 2.1Total Physical Product (TPP), Marginal Physical Product (MPP), Marginal Revenue Product (MPR) of
Total value of Farm (P × Q) 3850 × $ 40 $ 154,000Conclusions: Because of inflation, the price of rye and wage rate increased simultaneously. In the same way,
the marginal revenue to the Farm and wages to labourers also increased. With the rise in prices, the purchasing power of consumers decreases. But the inflation has also
increased the revenue to the farmers and wages to the labourers, their standard of living will be unchanged.
If the prices of the goods bought by Wry Islanders rise eleven fold (or nine fold), the revenue and wage rate also change proportionately. In the same way, the standard of living will be unchanged.
In general inflation, with increase in price level, revenue does not increase proportionately. As such, the living standard will be decreased.
Therefore uneven rise in price affect the wage rate and rent earned on the farms.
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[III] Growth of Factor Inputs (a)In case of adding new labourers in Wry Island, the total number of labourers will increase causing increase in supply of labour. With 20 labourers, the new equilibrium wage rate will be $800.
Conclusions: With increase in supply of labour, the wage rate has decreased to $800. However, the total wage income has increased from $ 11700 to $ 16,000. The total rent income also increased from $ 3700 to $ 10,000, labourers' share of income is 61.54% ($ 16,000/$ 26,000), and total income is $ 26,000.
[III] Growth of Factor Inputs (b)When one of the sailors, named Dalta, turned into gentle wo(men), the total number of laborers decreased to 19. The new equilibrium wage rate of the 19 laborers is $ 1100.
Table 3.2(b)Allocation of Resources and Distribution of Income
Units ComputationRye only @ $4 per bu. 19
workerWages rate $ $ 1,100Farm A:
Workers No. 3Rent $ (1000 × $ 4 – 3 × $
1100)$ 700
Farm B:Workers No. 6Rent $ (2725 × $ 4 – 6 × $
1100)$ 4,300
Farm C:Workers No. 4Rent $ (1250 × $ 4 – 4 × $
1100)$ 600
Farm D:Workers No. 6Rent $ (2725 × $ 4 – 6 × $
1100)$ 4,300
Total wages bill (A + B + C + D)
19 × $ 1100 $ 20,900
Total rent $ 700 + $ 4300 + $ 600
$ 9,900
Total Farm income (wages & rent)
$ 30,800
Total value of Farm (P × Q) 7700 × $ 4 $ 30,800
Conclusions:
With 19 laborers, the total value of output increased from $ 26,000 to $30,800, wage rate also increased from $800 to $1,100. Similarly, the total wages also increased from $16,000 to @20,900. However, the total rent decreased from $10,000 to $9,900.
[III] Growth of Factor Inputs (c)
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According to Malthus and Ricardo’s Theory of Rent, with the population growth, the supply in labor also increases. But the other factor of production – technology and capital stock–remains constant. Though, increase in labour increases production, but it decreases at some level of production. Therefore, the over supply of labour will ultimately decreases the wage rate. Hence, increased production will increase the rent to the landlord but increase of labur will decrease the wage to the labourers.
Table 4.2 (b) Allocation of resources and distribution of income
Units ComputationsRye @ $4/bu. and Rice $
5.5/bu.Wages rate $ $ 1,100Farm A:
Workers No.Rent $ (1000 × $ 4 – 3 × $
1100)$ 700
Farm B:Workers No. 3Rent $ (2725 × $ 4 – 6 × $
1100)$ 4,300
Farm C:Workers No. –Rent $ (3625 × $ 4 – 5 × $
1100)14,438
Farm D:Workers No. 3Rent $ (2725 × $ 5.5 – 6 × $
1100)$ 4,300
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Total wages bill (A + B + C + D)
$ 22,000
Total rent $ 23,738Total Farm income (wages & rent)
$ 45,738
Total value of Farm (P × Q) $ 45,738
Conclusions:
With increase in price of rice to $ 5.50, the total rent earned by producing rice increased to $ 14,438 from $ 1100. This will definitely encourages producing rice instead of rye.
[V] Industrialization
New equilibrium wage = $ 1900Table 5.1Total Physical Product (TPP), Marginal Physical Product (MPP), Marginal Revenue Product (MPR) of