Suppose it is a hot summer

Economics Oct 21, 2020

Suppose it is a hot summer. Jane just bought a five-bedroom apartment and would like to install air-condition (AC) for each room. Here is the value she places on the AC (including installment fee) for her five rooms (assume the rooms are homogeneous): Value of first AC 5000 (yuan) Value of second AC 4000 Value of third AC 3000 Value of fourth AC 2000 Value of fifth AC 1000 • From this information, derive her demand schedule and graph her demand curve for AC installment. • If the price of each unit of AC is 5000 (yuan), how many units of AC does Jane would like to install? How much consumer surplus (CS) does Jane get from her purchases? Please show her cosumer surplus in your graph. • Suppose the cost falls to 2000(yuan),how many units of AC does Jane would like to install? How much consumer surplus does Jane get from her purchases? • Generally, when the cost of AC falls, how will the CS change and why?
Suppose John owns a home appliance shop. Because AC installment is a labor-intensive practice, the cost of installing a unit of AC rises as he sells and installs more. Here is the cost he incurs to install each unit of AC: Value of first AC 1000 (yuan) Value of second AC 2000 Value of third AC 3000 Value of fourth AC 4000 Value of fifth AC 5000 • From this information. derive his supply schedule and graph his supply curve for AC installment. • If the market price of each unit of AC (including installment cost) is 5000 (yuan), how many units of AC does John would like to sell and install for Jane? How much producer surplus (PS) does John get from these sales? Please show his producer surplus in your graph. • Suppose the price falls to 1000(yuan), how many units of AC does John would like to sell and help install? How much producer surplus does John get from these sales? • Please use Jane's demand schedule and John's supply schedule to find the market equilibrium price and quantity? Graph the market supply and demand curve (linear curve), and point out the equilibrium point. • What are consumer surplus, producer surplus, and total surplus in this equilibrium? Please show them in your graph. Suppose this summer is the hottest on record, Jane's willingness-to-pay for each AC increases 2000. Please find the new market equilibrium price and quantity? Graph the market supply and demand curve (linear curve), and point out the equilibrium point. What are consumer surplus, producer surplus, and total surplus in this equilibrium? Now suppose the summer is normal, and Jane's WTP for the AC remains the initial condition. Suppose the government tax the purchase of AC (carbon emission fee) and require appliance dealers to pay the government 200 (yuan) for each AC sold. Graph the change of consumer surplus, producer surplus, and total surplus both before and after the tax, and finish the table (hint: check the slide of lecture3, for this question, there is no need to calculate the value ):

Expert Solution

Demand Schedule :

Quantity in units	price in $
1	5000
2	4000
3	3000
4	2000
5	1000

First AC is bought when p = $5000 , but at $5000 only one AC will be bought. Only when price = $4000 , Jane will buy 2 AC . Similarly 3 ACs will only be bought when price drops to $3000 . This is the logic behind demand schedule.

Demand curve is shown by fig 1

Fig 1

When price is $5,000 , Jane will buy 1 AC . Her willingness to pay for second AC < $5,000 , so Jane won't buy more than 1.

Consumer surplus = price Jane was willing to pay for first AC - price of first AC = $5000 - $ 5000 = 0 .

In graph, consumer surplus is the area above price line enclosed between demand curve and price line . Here p= $ 5000 . We can see from figure 2, relevant area is zero.

Fig 2

When price falls to $2000 , Jane can install upto 4 AC. Hence, demand for AC at this price is 4.

Since price is $2000 , every unit of AC will be sold at $2000 only. For the first unit Jane was willing to pay $5000 and for second $4000 ,for third $3000, Now she gets all these units at $2000, which means she is enjoying surplus. Surplus is the difference in her Willingness to pay and the amount she actually pays

Consumer surplus = Willingness to pay for first unit + willingness to pay for second unit + willingness to pay for third unit + willingness to pay for fourth unit - Amount she actually pays for 4 units

= ${ 5000+4000+3000+2000 - 4*2000 } = $ 6000

In fig 3 , the shaded area represents consumer surplus

Fig 3

When cost of AC falls , consumer surplus increases. Consumer surplus happens when cost incurred by the consumer is lesser than her willingness to pay. The more is the difference, greater is the value of consumer surplus. And as price falls the difference between willingness to pay and price increases, hence consumer surplus increases.

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