homework 1 assignment for mgec PDF

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MGECHW1 Answer KeyProblem 1 A computer products retailer purchases laser printers from a manufacturer at a price of Rs. 25, per printer. During the year, the retailer will try to sell the printers at a price greater than Rs. 25,000, but may not be able to sell all the printers. At the end of the yea...

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MGEC HW1 Answer Key Problem 1 A computer products retailer purchases laser printers from a manufacturer at a price of Rs. 25,000 per printer. During the year, the retailer will try to sell the printers at a price greater than Rs. 25,000, but may not be able to sell all the printers. At the end of the year, the manufacturer will buy back any unsold inventory at 40 percent of the original price. No one other than the manufacturer would be willing to buy these unsold printers at the end of the year. a) At the beginning of the year, before the retailer has purchased any printers, what is the opportunity cost of a laser printer? Since a printer costs Rs. 25000, before purchasing any printers, the opportunity cost of a laser printer would be the next best use of Rs. 25000 for the retailer. For example, this money could be invested elsewhere at a certain rate of return. This return foregone would be the opportunity cost of the laser printer. b) After the retailer has purchased the laser printers, what is the opportunity cost associated with selling a laser printer to a customer? (Assume that if this customer does not buy the printer, it will be unsold at the end of the year.) Any unsold inventory will be bought back by the manufacturer at 40% of the original price; Rs.10,000 (25000*.40). Therefore, the opportunity cost associated with selling a laser printer to a customer would be Rs. 10,000 as this is the next best alternative available to the retailer. c) Suppose that at the end of the year, the retailer still has a large inventory of unsold printers. The retailer has set a retail price of Rs. 30,000 per printer. The manager of the store proposes that they should cut the price by half and sell the printers at Rs. 15,000 each. The owner of the store disagrees, pointing out that at Rs. 15,000 each, they would lose Rs. 10,000 on each printer sold. Is the owner’s argument correct? No, the owner has fallen prey to the sunk cost fallacy. He is anchored to the purchase price of Rs. 25000, and is considering sale of printers at Rs. 15000, as a situation where he would incur a loss of Rs. 10,000 (Purchase price-offer price; 25000-15000). When in fact, he should be comparing the following two situations;  cutting the price by half and selling the printers at Rs. 15,000 each  unsold printers being bought back by manufacturer at Rs. 10,000 each. Clearly, the best alternative available to him at this juncture is to select the first option, where he would actually be cutting his losses by Rs. 5000.

Problem 2 Consider the demand curve for the latest wearable fitness device, QD = 40,000 - 4P. a) Plot the demand curve Q = 40000-4P

b) Find the price and quantity at which the demand is unit elastic Given that price elasticity of demand (ϵd ) = -1 Demand curve:

Q= 40000− 4 P

dQ =−4 dP ϵd =

dQ × dP

-1 = −4 ×

P Q

P 40000−4 P

Solve for P. P= 5000. To find Q, plug P=Rs. 5000 in the demand equation Q = 40000-4P; Q = 20000. Demand is unit elastic at Price = Rs. 5000 and Q = 20000 c) Compute the elasticity of demand when the staring price is i. Rs. 2,000 Given, P = Rs. 2000. We can find the corresponding quantity (Q), by plugging P=Rs. 2000 in the demand equation Q = 40000-4P; Q = 32000 Use price elasticity formula to find ϵd

ϵd =

dQ × dP

P Q

ϵd =

−4 ×

2000 32000

ϵd = ii.

−1 4

or -0.25

Rs. 1,000 Given, P = Rs. 1000. We can find the corresponding quantity (Q), by plugging P = Rs. 1000 in the demand equation Q = 40000-4P; Q = 36000 Use price elasticity formula to find ϵd ϵd =

dQ × dP

P Q

ϵd =

−4 ×

1000 36000

ϵd =

−1 9

or -0.11

Problem 3 The demand for beer in Gachibowli is given by: QD = 700 - 20P – 10Pc + 0.1I, where P is the price of beer, Pc is the price of chips, and I is the average consumer income. a) Please provide an expression for the elasticity of demand for beer with respect to the price of chips. Based on your answer, are beer and chips complements or substitutes? Cross Price elasticity of demand for beer with respect to the price of chips ( ϵbc) can be written as: ϵbc =

dQ × dPc

Pc Q

or ϵbc =

−10 ×

Pc Q

Beer and Chips are complementary goods since ϵbc is negative, indicating an inverse relationship between price of chips and demand for beer. If price of chips goes up (down), the demand for beer decreases (increases). b) Calculate the own price elasticity, the cross price elasticity and the income elasticity of the demand for beer when P = 50, Pc = 15, and I = 14,000 Given demand function: Q = 700 - 20P – 10Pc + 0.1I and P = 50, Pc = 15, and I = 14,000. Plugging these values into the demand function: Q = 700 – 20 (50) – 10 (15) + 0.1 (14000) Q = 950 Price Elasticity at P = 50

P Q 50 ϵd = −20 × 950 ϵd = −¿ 1.053 ϵd =

dQ × dP

Cross price elasticity at Pc = 15

ϵxy =

dQ × dPc

ϵxy = −10 × ϵxy =

Pc Q

15 950

−¿ 0.158

Income elasticity at I = 14000

dQ I × Q dI 14000 ϵI = 0.1 × 950

ϵI =

ϵI = 1.473 c) Graph the demand curve for beer when Pc = 15, and I = 14,000 Given demand function: Q = 700 - 20P – 10Pc + 0.1I and given Pc = 15, and I = 14,000. Plugging these values in the demand function: Q = 700 – 20P – 10(15) +0.1(14000) Q = 1950 – 20P Q = 1950-20P

Problem 4 The demand curve for pedicures is given by: QD = 20 - 4P + 0.2I, where P is the price of a pedicure, and I is the average consumer income. a) Assume that I is 400. What is the consumer surplus when P is 15? By how much does the consumer surplus change if P falls to 10? Given demand function: Q = 20 - 4P + 0.2I At I = 400; demand function can be written as; Q = 20 – 4P + 0.2 (400); Q = 100-4P At P = 15; Q can be found by plugging this value in the demand function; Q = 100-4P Q = 100 – 4 (15) Q = 40 This can be shown graphically as: Q = 100-4P

Consumer surplus is given by the area of the triangle; above market price (P=15) 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 40 and the height is 10 (25-15), therefore

1 Consumer Surplus= × 40 × 10=200 2 By how much does the consumer surplus change if P falls to 10? When P falls to 10; Q can be found by plugging this value in the demand function; Q = 100-4P Q = 100 – 4 (10) Q = 60 In this case, consumer surplus is given by the area of the triangle; above market price (P=10) and below the demand. In this case, the base is 60 and the height is 15.

1 Consumer Surplus= ×60 ×15 =450 2 Change in consumer surplus = 450 – 200 = 250 This can be shown graphically as: Q = 100-4P

b) At a market price of 20, what is the pedicurist’s income? Suppose the pedicurist wants to increase her income. Should she increase or decrease the price of a pedicure? Demand function: Q = 100-4P (Assuming I = 400) At P = 20; Q can be found by plugging this value into the demand function, Q = 100 - 4P; Q = 100 – 4(20) Q = 20 Pedicurist’s income = Price ×

Quantity = 20

× 20 = 400

To increase her income, the pedicurist should decrease the price of a pedicure, if the demand curve is relatively elastic; ϵd >1. If demand curve is relatively inelastic; ϵd 1, (consider absolute value), hence the demand curve is relatively elastic; a change in price will lead to proportionately greater change in quantity demanded and therefore, an increase in income. Therefore, the pedicurist should decrease the price of a pedicure in order to increase her income.

c) Assume now that income increases to 500. What is the consumer surplus at P = 15? Demand Function: Q = 20 - 4P + 0.2I At I = 500; demand function can be written as; Q = 20 – 4P + 0.2 (500); Q = 120-4P At P = 15; Q can be found by plugging this value in the demand function; Q = 120-4P Q = 120 – 4 (15) Q = 60 Consumer surplus is given by the area of the triangle; above market price (P=15) 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 60 and the height is 15 (30-15), therefore

1 Consumer Surplus= ×60 ×15 =450 2 This can be shown graphically as: Q = 120-4P

Problem 5 Suppose you are analyzing the demand for buttermilk at the Goel dining hall. Consider each of the following scenarios and explain whether it would lead to an increase, decrease, or no change in demand: a) Term break – Decrease in demand b) A thunderstorm that brings down the temperature by several degrees – Decrease in demand c) A decrease in the price of buttermilk – No change in demand, decrease in price of buttermilk will cause increase in quantity demanded d) A decrease in the price of watermelon juice – Decrease in demand e) A decrease in the price of photo copying – No change in demand f) The latest campus fad – “veganism” – Decrease in demand Problem 6 Suppose there are 2 countries, X and Y, capable of producing 2 goods: sense and nonsense. The output per worker in Country X is 8 units if the worker produces sense and 4 units if he/she produces nonsense. In Country Y, the output per worker is 6 units of sense or 2 units of nonsense. What is the pattern of absolute and comparative advantage? Opportunity cost of Opportunity cost of sense nonsense in terms of sense Sense Nonsense in terms of nonsense given given up up X 8 4 1/2 2 Y 6 2 1/3 3 Absolute Advantage: Country X has the absolute advantage of producing both sense and nonsense because X uses fewer inputs to produce each of these relative to Y. Comparative Advantage: X has a lower opportunity cost in producing nonsense and Y has a lower opportunity cost in producing sense. Hence X has a comparative advantage in producing nonsense and Y has a comparative advantage in producing sense....