Question

Beth is a second-grader who sells lemonade on a street corner in your neighborhood. Each cup of lemonade costs Beth $0.20 to produce; she has no fixed costs. The reservation prices for the 10 people who walk by Beth's lemonade stand each day are listed in the following table.

Person	1	2	3	4	5	6	7	8	9	10
Reservation price	$0.50	$0.45	$0.40	$0.35	$0.30	$0.25	$0.20	$0.15	$0.10	$0.05

Beth knows the distribution of reservation prices (that is, she knows that one person is willing to pay $0.50, another $0.45, and so on), but she does not know any specific individual’s reservation price.

a. Calculate the marginal revenue of selling an additional cup of lemonade. (Start by figuring out the price Beth would charge if she produced only one cup of lemonade, and calculate the total revenue; then find the price Beth would charge if she sold two cups of lemonade; and so on.)

Price	Quantity	Total revenue ($ per day)	Marginal revenue ($ per cup)
0.50	1
0.45	2
0.40	3
0.35	4
0.30	5
0.25	6
0.20	7
0.15	8
0.10	9
0.05	10

b. What is Beth’s profit-maximizing price?

Instruction: Enter your response rounded to two decimal places.

$ .

c. At that price, what are Beth’s economic profit and total consumer surplus?

Instruction: Enter your responses rounded to two decimal places.

Economic profit: $ per day.

Consumer surplus: $ per day.

d. What price should Beth charge if she wants to maximize total economic surplus?

Instruction: Enter your response rounded to two decimal places.

Price to maximize total economic surplus: $ .

Answer 1

a.

Price	Quantity	Total Revenue	Marginal Revenue	Total Cost	Marginal Cost
P	Q	P*Q	TRn-TRn-1	0.2 * Q	TCn - TCn-1
0.5	1	0.5 ( 0.5 * 1)	0.5	0.2
0.45	2	0.9	0.4 ( 0.9 -0.5 )	0.4 ( 0.2 * 2 )	0.2 ( 0.4 -0.2)
0.4	3	1.2	0.3	0.6	0.2
0.35	4	1.4	0.2	0.8	0.2
0.3	5	1.5 ( 0.3 * 5 )	0.1 ( 1.5 - 1..4)	1 ( 0.2 * 5 )	0.2 ( 1- 0.8 )
0.25	6	1.5	0	1.2	0.2
0.2	7	1.4	-0.1	1.4	0.2
0.15	8	1.2	-0.2	1.6	0.2
0.1	9	0.9 ( 0.1 * 9 )	-0.3 ( 0.9 -1.2 )	1.8 ( 0.2 * 9 )	0.2 ( 1.8 - 1.6 )
0.05	10	0.5	-0.4	2	0.2

b.

The condition for profit -maximization is where , MR=MC

in the above table it can be observed that quantity 4 , MR=MC=0.2

So, $0.35 is the profit maximization price.

c.

At $ 0.35

Profit = Total Revenue - Total Cost = 1.4 - 0.8 = $0.6

Consumer Surplus

So, to calculate consumer surplus , the area of triangle ABC needs to be calculated

= 1/2 * CB * AC

= 1/2 * 4 * ( 0.55-0.35)

= 1/2 * 4 * 0.2

= $0.4

SO,

Profit = $0.6

Consumer Surplus = $0.4

d.  

Demand	Q	Supply
0.5	1	0.2
0.45	2	0.25
0.4	3	0.3
0.35	4	0.35
0.3	5	0.4
0.25	6	0.45
0.2	7	0.5
0.15	8	0.55
0.1	9	0.6
0.05	10	0.65

If , beth is selling only one cup, then she would want to recover her total cost at $0.2 and for every additional lemonade she adds $0.05 to the existing price.

Total economic surplus is maximized when , the price is equal to the equilibrium price otherwise shortages or excess can affect the total economic surplus.

So, at price $0.35 the total economic surplus would be maximum.