Question

1. A price response function is d(p) = 8000 – 200 p. If the unit price is $10, what is the point elasticity at this price? What if the unit price is $20? b. A new laptop’s production cost is $400. Its current retail price is $500. At this price, the price elasticity is c. Is the current price optimal? Should the company increase or decrease its price? What is the optimal price? The current price is not optimal as price elasticity is way to high meaning that as price increases demand will most likely decrease which is not good. An optimal price would reflect a price elasticity of 0 meaning that it has little to no effect on demand. I think that the laptop c. A manufacturer faces a linear price response function d(p)=8000 – 200p. The unit production cost is $10. The manufacturer’s capacity is 6000 units. What is the optimal price? What is the total profit of the manufacturer? d. A major machine breakdown reduces the manufacturer’s capacity to 2000 units. What is the optimal price now? Does reducing capacity always result in increasing optimal price? 2. A manufacturer faces a linear price response function d(p)=8000 – 200p. The unit production cost is $10. The manufacturer can segment market into two parts by promising different lead times. (1) If the separating price is at $30, what are the optimal prices for the two segments? What is the total profit? (2) If the separating price is at $20, what are the optimal prices for the two segments? What is the total profit?

Answer 1

1.

A.

Q = 8000-200*P

At P = $10

Q = 8000-200*10 = 6000

Further, dQ/dP = -200

Point elasticity = (dQ/dP)*(P/Q) = (-200)*(10/6000)

Point elasticity = -.33

At P = $20

Q = 8000 - 200*20 = 4000

Point elasticity = (dQ/dP)*(P/Q) = (-200)*(20/4000) = -1

B.

(P-MC)/P = -1/E

(500-400)/500 = -1/E

E = -5

The current price is not optimal because the product is highly elastic in nature. With slight increase in price, there will be sharp decrease in demand of the product.

Company should decrease the price to increase the demand and sales of the product.

At E = 0

(P-MC)/P = 0

P-MC = 0

P = MC

So, price should be equal to MC to make the demand indifferent to the elasticity. So, the company should put the price of $400 to make it equal to the MC.

C.

Q = 8000-200P

At Q = 6000

6000 = 8000-200P

P = 2000/200

P = $10

D.

If quantity of output comes down to 2000 units

2000 = 8000-200P

P = (8000-2000)/200

P = $30

No, it is the elasticity of demand, market structure and the status of economic profit in the market, that will decide the optimal price.

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