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Managerial Economics Indian School of BusinessHomework 2 Answer KeyProblem 1 The market demand for Economics textbooks is given by Q = 160 – 4P. Total cost of the firm is given by TC = 6Q 2 +15Q+ a) Find the profit maximizing level of output, price, and profit if this firm is the only firm in the ma...

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Managerial Economics Indian School of Business Homework 2 Answer Key Problem 1 The market demand for Economics textbooks is given by Q = 160 – 4P. Total cost of the firm is given by TC = 6Q2+15Q+5 a) Find the profit maximizing level of output, price, and profit if this firm is the only firm in the market. (3 Points) If this firm is the only firm in the market, it’s a monopoly. For obtaining profit maximizing level of output, set

MC = MR The demand curve is given by: QD = 160 – 4P, this can be expressed as:

P=40−

Q 4

Total Revenue(TR)=P× Q Q TR=Q(40− ) 4

TR=40 Q−

MR=

Q2 4

dTR dQ

MR=40−

2Q 4

MR=40−

Q 2

Marginal Cost (MC) can be obtained by differentiating the total cost function with respect to Q 2

TC=6 Q + 15Q +5 MC=12 Q+ 15 Profit will be maximized at

1

MC = MR

12 Q+ 15 =40 −

Q 2 Solving for Q, Q = 2

Profit maximizing price can be found by plugging Q=2 in the demand function;

P=40−

Q 4

P = 39.5

Profit ( π )=TR −TC

TR=40 Q−

Q2 4

TC=6 Q 2+15Q+5 Plugging the value of Q = 2 in the above equations, TR = 79 and TC = 59

Profit ( π )=79 −59 Profit ( π )=20 b) Find the short-run profit maximizing level of output and profit of the firm assuming the market is perfectly competitive and the market price is 27. (2 Points) In perfect competition, P=AR=MR. As calculated in part (a), MC=12 Q+15 For a firm in perfect competition, the short-run profit maximizing level of output can be found by setting

MC = MR 12 Q + 15 =27

Q=1 Profit ( π )=TR −TC TR=P ×Q = 27

TC=6 Q 2+15Q+5 TC=26 Profit ( π )=27 −26 Profit ( π )=1 2

×1= 27

c) If the market is perfectly competitive and the market price is 75, what will happen in the long run? (1 Point) The economic profit for a perfectly competitive firm, in equilibrium is 0. Increasing the price to 75 in the short run, will lead to even higher profits (than at the price level of 27) and many firms will enter the industry and drive the price down till it reaches a price level corresponding to zero economic profits. Just to corroborate; if the market price is 75, then again the short-run profit maximizing level of output would be found by setting

MC = MR

12 Q+ 15 =75 Q=5 Profit ( π )=TR −TC TR=P ×Q = 75

×5=375

2

TC=6 Q + 15Q +5 TC=230

Profit ( π )=375−230 Profit ( π )=145 Since firms are earning economic profit, more firms will enter the market and drive the price down to the level where industry is in long term equilibrium.

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Problem 2 Consider the market for biryani in Hyderabad. In this market, the supply curve is given by Qs = 10PB − 5PR and the demand curve is given by QD = 100 − 15PB + 10PK , where B denotes biryani, R denotes rice, and K denotes kebabs. a) Assume that PR is fixed at 1 and PK = 5. Calculate the equilibrium price and quantity in the biryani market. What is the producer and consumer surplus generated by the biryani market at these prices? (1+1.5+1.5 points) If PR = 1 and PK = 5, the demand curve can be rewritten as: QD = 150 − 15PB and the supply curve can be rewritten as Qs = 10PB – 5 Equilibrium price and quantity can be calculated by equating the demand and supply curves:

150−15 PB =10 PB – 5 PB =6.2 Plug this value into demand curve to get equilibrium quantity: QD = 150 – 15 (6.2)

Q D =57 Consumer and Producer Surplus can be shown graphically as:

Q D =150 −15 P B Q S =10 P B – 5

Consumer surplus is given by the area of the triangle; above market price (P=6.2) and below the demand curve. We can use the formula for area of a triangle =

1 ×base ×height 2

to calculate the consumer

surplus. In this case the base of the triangle is 57 and the height is 3.8 (10-6.2), therefore 4

1 Consumer Surplus= ×57 ×3.8 =108.3 2 Similarly, producer surplus is given by the area of the triangle; below market price (P=6.2) and above the supply curve. We can use the formula for area of a triangle =

1 ×base× height 2

to calculate the

producer surplus. In this case the base of the triangle is 57 and the height is 5.7 (6.2-0.5), therefore

1 Producer Surplus= ×57 ×5.7 =162.45 2 b) Suppose that a poor harvest season raises the price of rice to PR = 2. The price of kebabs remains the same as in part a. Find the new equilibrium price and quantity of biryani. Draw a graph to illustrate your answer. (2 points) Given that PR = 2, new supply curve for biryanis can be rewritten as; Qs = 10PB – 10 The demand curve remains the same; QD = 150 − 15PB Equilibrium price and quantity can be calculated by equating the demand and supply curves:

150−15 PB =10 PB – 10 PB =6.4 Plug this value into demand curve to get equilibrium quantity: QD = 150 – 15 (6.4)

Q D =54 This can be shown graphically as:

5

Q D =150 −15 P B Q S =10 P B – 10

c) Suppose PR = 1 but the price of kebabs drops to PK = 3. Find the new equilibrium price and quantity of biryani. (2 points) At PK = 3, the demand curve can be rewritten as QD = 130 − 15PB while the supply curve remains the same; Qs = 10PB – 5 Equilibrium price and quantity can be calculated by equating the demand and supply curves:

130−15 PB =10 PB – 5 PB =5.4 Plug this value into demand curve to get equilibrium quantity: QD = 150 – 15 (5.4)

Q D =49 d) Suppose PR = 1, PK = 5, and the local government mandates that since a lot of tourists like to eat biryani when they visit Hyderabad, in the interest of promoting tourism, the price of biryani cannot exceed 5. How much is the shortage of biryani as a result? Draw a graph to illustrate your answer. (2 points) As in part (a), if PR = 1 and PK = 5, the demand curve will be: QD = 150 − 15PB and the supply curve will be Qs = 10PB – 5 Given that plugging

PB =5 as mandated by the government. Quantity demanded and supplied can be found by PB =5 in the demand and supply equations. 6

Q D =75 Q S =45 Shortage =30 units This can be illustrated graphically as:

Q D =150 −15 P B Q S =10 P B – 5

7

Problem 3 The market demand curve for a monopolist is given by P = 40-2Q. a) What are the marginal revenue and average revenue functions for the firm? (2 points) Average Revenue = Price function; AR =40−2 Q

Total Revenue(TR)=P× Q TR=Q(40−2Q) TR=40 Q−2 Q

MR=

2

dTR dQ

MR =40−4 Q b) What will be the profit maximizing price and quantity for this firm if average cost is given by Q? (1 point) If AC = Q, Total Cost = AC × Q = Q2

MC=

dTC dQ

MC =2 Q The monopolist maximizes profits at

MC = MR

2Q =40−4 Q 20 Q= 3 Price can be found by plugging this value in the demand equation; P = 40-2Q

P=

80 3 Thus, the monopolist maximizes profits at price of 80/3 and quantity of 20/3

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Problem 4 It is lunch time and there are 2 kinds of customers at the Goel dining hall: students from the afternoon sections, and students from the morning sections. Their respective demand curves for lunch per week are given by QA = 800 – 2P and QM = 920 – 4P. The dining hall’s marginal cost of each lunch served is 30. a) Assume that the dining hall can price discriminate. What is the profit maximizing price that the dining hall can charge from each type of student? (4 points) Method 1: Recall that the mark-up that a firm can charge over the marginal cost is given by:

−1 ∈D P∗− MC∗¿ ¿ ¿ P∗¿=

dQ × dP

Where ϵd =

P Q

Since the dining hall can price discriminate, it will charge each type of student a mark-up that is the inverse of their elasticity of demand. Let the price charged to the afternoon section students be PA and the price charged to the morning section students be PM. Therefore for the afternoon section students, PA can be found by plugging the values MC = 30 and

dQ =−2 and Q = QA = 800 – 2PA in the equation: dP P A −MC −dP Q = × PA dQ P P A −30 −1 800 – 2 P A ) × =−( PA PA 2 P A −30= 400− P A P A =Rs . 215

Similarly, for the morning section students, PM can be found by plugging the values MC = 30 and

dQ =−4 and Q = QM = 920 – 4PM in the equation: dP P M −MC −dP Q = × P dQ PM 9

P M −30 −1 920 – 4 P M =−( ) × PM PM 4 PM −30=230−PM PM =Rs .130 Morning section students are being charged Rs. 130 and afternoon section students are charged Rs. 215 Method 2: We can also find profit maximizing price and output by setting MRM = MRA = MC Given Demand curves: QA = 800 – 2PA and QM = 920 – 4PM Rewriting the demand curves:

QA 2 QM PM =230 – 4 P A =400 –

TR = P ×Q

and MR =

dTR dQ

Therefore, MRA = 400 - QA

And MRM = 230 –

QM 2

Setting MRA = MC; 400 - QA = 30; QA = 370; Plug this value into the demand function;

P A =400 –

370 2

P A =215 Similarly, setting MRM = MC; 230 –

PM =230 –

QM 2

= 30; QM = 400; Plug this value into the demand function;

400 4

PM =130

b) Why do you think the elasticity of demand is different for the two types of students? (2 points) Afternoon section students are time constrained as their classes start from 1:15 pm. Hence, their demand curve is less elastic compared to morning section students, who are done with their classes by lunch time. 10

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Problem 5 Suppose that the market for calcium is perfectly competitive. Consider the following information about its price: • Between 2000 and 2005, the market price was stable at about Rs. 200 per kilo. • In the first 3 months of 2006, the market price doubled, reaching a high of Rs. 400 per kilo, where it remained for the rest of 2006. • Throughout 2007 and 2008, the market price of calcium declined, eventually reaching Rs. 200 per kilo by the end of 2008. • Between 2008 and 2013, the market price was stable at that level Assuming that the technology for producing calcium did not undergo any changes between 2000 and 2013, and the input prices faced by calcium producers remained constant, what explains the pattern of prices that prevailed between 2000 and 2013? Is it likely that there were more producers of calcium in 2013 than there were in 2000? Explain your answers using graphs. (2 + 1 + 3 points) Summary Time Period

Market Price

Implication

2000-2005

Stable at Rs. 200 per kilo

Industry is in long run equilibrium

2006

Doubled to Rs. 400 per kilo

2007-2008

Declined and reached Rs. 200 per kilo

2008-2013

Stable at Rs. 200 per kilo

Given that there was no change in technology or input prices faced by calcium producers, we can safely assume that market price increased due to increase in demand. Surge in demand leads to economic profits for firms in the industry. Market demand curve shifts outwards to MD1 (refer to figure 2) leading to a higher price. More firms enter the market to take advantage of high prices and earn economic profits. However, with increasing number of firms in the market, supply gradually catches up, market supply curve moves outwards to MS1 (refer to figure 3) and price declines to long run equilibrium level. Industry is in long run equilibrium. It can be said with certainty that there were more producers of calcium in 2013 than there were in 2000.

Figure 1: Perfectly competitive market for Calcium from 2000-2005 and 2008-2013

MS

Price

Price

Time Period: 2000-2005 and 2008-2013 MC AC

AR=MR

200

200

MD Quantity Market Demand and Supply

Quantity Individual Firm

Figure 2: Perfectly competitive market for Calcium for 2006 Price

Price

Time Period: 2006 MC

MS

AC 400

400

Economic Profits AR=MR

200

200 MD1

MD Quantity

Quantity

Market Demand and Supply

Individual Firm

13

Figure 3: Perfectly competitive market for Calcium from 2007-2008 Price

Price

Time Period: 2007-2008

14

MC

Problem 6 Suppose that Air India has a monopol MS he route between Delhi and Srinagar. During the winter months, the monthly demand on this route is given by P MS1 Q; and during the summer months, it is give AC a – bQ, where a2 > a1. Assume that Air India’s marginal cost is constant, and is given by c. 400 ll be the equilibrium price and quantity in each season? (4 points) 200

To find the equilibrium price and quantity in each 200 Air India will equate MR for winter mo AR=MR MR for summer months to marginal cost; MRS = MRW = MC For winter months, monthly demand i MD1

y the equation: P = a1 – bQ

MD

Total Revenue(TR)=P× Q

Quantity

Quantity

Market Demand and Supply

Individual Firm

TR= a1 Q −bQ2 MR=

dTR dQ

MR =a1−2 bQ Profit is maximized at MR = MC, where MR is given above and MC = c

a1−2bQ =c

Equilibrium quantity in winters is

Q=

a1−c 2b

Equilibrium price in winters can be found by plugging this value in the demand function; P = a1 – bQ

P=a1−b(

P=

a 1−c ) 2b

a1 +c 2 Likewise, for summer months, monthly demand is given by the equation: P = a 2 – bQ

Total Revenue(TR)=P× Q TR=Q( a 2−bQ ) TR=a2 Q −bQ

2

15

MR=

dTR dQ

MR =a2−2 bQ Profit is maximized at MR = MC, where MR is given above and MC = c

a2−2 bQ =c Equilibrium quantity in summers is

Q=

a2 −c 2b

Equilibrium price in summers can be found by plugging this value in the demand function; P = a2 – bQ

P=a2−b (

P=

a2−c ) 2b

a2 +c 2

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Problem 7 [12 points] Consider the labor market and specifically the demand and supply for unskilled workers. Assume that the market is competitive. The labor supply and labor demand curves are as follows: Ls = 10W – 1,000 Ld = 3,000 – 10W Where, L is measured in terms of number of workers and W is the wage rate paid to each worker per day (in Rs). a. What is the market clearing wage and employment that would exist in equilibrium? [1 point] b. The current minimum wage for unskilled workers is Rs 180 per day. What impact does this minimum wage on the market? [1 point] c. The government is considering increasing the minimum wage to Rs. 220 per day. Calculate the impact of the proposed minimum wage on the quantity of labor that will be demanded and supplied at this revised minimum wage. [2 points] d. Calculate the producer surplus (workers’ surplus) at the market clearing wage rate and under the proposed Rs 220 minimum wage. [2 points] e. What is the effect of the proposed minimum wage on individual workers vis-à-vis the net effect on unskilled workers as a whole? No additional calculations are required to answer this part of the question. Explain your answer in no more than 1-2 sentences. [2 points] f. How would this minimum wage policy differ from a minimum support price program for workers. Support prices are often used in agriculture but if a similar program was operationalized in the labor market would your answer to part (d) change? No additional calculations are required to answer this part of the question. Explain your answer in no more than 1-2 sentences. [2 points] g. Are either of the policies (minimum wage or price support) efficient from an economist's point of view? No additional calculations are required to answer this part of the question. Explain your answer in no more than 1-2 sentences. [2 points] Answer: a. Equate LD to Ls: 3000 – 10W = 10W – 1000 20W= 4000 W* = Rs 200 per day [0.5 point] L* = 3000 – 10(200) = 1000 workers Or, L* = 10(200) – 1000 = 1000 workers [0.5 point] b. No effect of minimum wage because Rs 180 is lower than W*. [1 point]

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Or, A minimum wage of Rs 180 per day would not be binding, and therefore the market would attain its free market equilibrium. [1 point] c. At the Rs 220 proposed minimum: LD = 3000 - 10(220) LD = 800 LS = 10(220) - 1000 LS = 1200 Ld = 800 and Ls = 1200 [2 points] The new minimum wage would create unemployment of 400 workers. [2 points] d. Rewrite LS and LD with W on left-hand side: LD = 3000 – 10W Or,

W = 300 – 0.1 LD LS = 10W – 1000

Or,

W = 100 + 0.1 LS

wage

300

220 200 180

100

800

1000

Original producer surplus at market clearing wage: Old P. S. = 0.5 × (200 – 100) × 1,000 = 50,000 [1 point] Determine reservation wage when there are 800 workers in the market W = 100 + 0.1(800) W = 180 Producer surplus at Rs 220 wage: New P. S. = 0.5 × (180-100) × 800 + (220-180) × 800 = 64,000 [1 point] 18

PS at original market clearing wage is Rs 50,000 and PS under proposed minimum wage is Rs 64,000. [2 points] Or, Workers as a whole have been made better off as indicated by the increase in producer surplus by Rs. 14,000 [2 points]

e. Individual workers who are displaced from labor force are worse off. Thus, some individual workers might suffer but overall, workers as a group benefit because the net change in producer surplus is positive. [1 point for yes/no, 1 point for explanation] f. Under minimum support price program, all workers would be better off unambiguously but that is not the case with minimum wage. Or, This policy differs from agricultural supports in that government does not buy up the surplus. When government buys the surplus, every producer is better off from the policy. [1 point for yes/no, 1 point for explanation] g. No, there is a loss in consumer surplus (employer surplus) that has not been calculated. When the loss in consumer surplus is accounted for, it is apparent that there is a deadweight loss from the minimum wage. Or, Any intervention that takes market away from W* and L* (the market clearing wage and employment) is inefficient because it imposes a deadweight loss. [1 point for yes/no, 1 point for explanation]

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