Question

Frank is an ice-cream maker in a monopolistic competitive market. He has developed a recipe using low-fat yogurt. Suppose that the marginal cost of producing one scoop of this special ice cream is $0.50, and there is no fixed cost. The demand for Frank’s special ice cream per hour is given by the table below.

Price	Quantity demanded
$2.50	0
$2.10	3
$1.70	6
$1.30	9
$1.00	12
$0.50	15
$0.00	18

            a.         How many scoops of ice cream should Frank produce in the short run to maximize profits? What price should he charge?         

            b.         Calculate Frank’s economic profits in the short run.                                

Price	Quantity demanded	TR	MR	MC	TC	Profit
$2.50	0
$2.10	3
$1.70	6
$1.30	9
$1.00	12
$0.50	15
$0.00	18

            c.         Lucy also has a special recipe to make low-fat ice cream. Suppose that her cost of making a scoop of ice cream is the same as Frank’s. Should she enter the market? Why or why not?                         

            d.         If Lucy enters the market, the demand for Frank’s ice cream will decrease by 2 at each price point. What are Frank’s new profit-maximizing quantity, price, and profits?                                                  

Price	Quantity demanded	TR	MR	MC	TC	Profit
$2.50	0
$2.10	1
$1.70	4
$1.30	7
$1.00	10
$0.50	13
$0.00	16

Answer 1

We can develop the following schedule based upon given information.

Price, P	Quantity demanded, Q	TR= P*Q	MR=Change in TR/Change in Q	MC	TC= MC*Q	Profit=TR-TC
2.50	0	0.00			0.00	0.00
2.10	3	6.30	2.10	0.50	1.50	4.80
1.70	6	10.20	1.30	0.50	3.00	7.20
1.30	9	11.70	0.50	0.50	4.50	7.20
1.00	12	12.00	0.10	0.50	6.00	6.00
0.50	15	7.50	-1.50	0.50	7.50	0.00
0.00	18	0.00	-2.50	0.50	9.00	-9.00

a)

Frank will continue to increase production as long as MR is higher than MC or MR is equal to MC to maximize the profit.

We can observe that MR=MC for Q=9. At Q=12, MR<MC. So, optimal output is 9 units.

Frank should produce 9 units at a price of $1.30 to maximize the profit.

(We can see that Profit is same as optimal profit at output level of 6 units. Price is $1.70 at this output. In such case, we prefer higher output at. lower price i.e 9 units, However output of 6 units is equally profitable)

b)

Refer to above table, optimal profit is $7.20 at a output level of 9 units.

c)

Frank is making profit. Lucy should enter into market as it is profitable in current situation.

d)

Price, P	Quantity demanded, Q	TR= P*Q	MR	MC	TC= MC*Q	Profit=TR-TC
2.50	0	0.00			0.00	0.00
2.10	1	2.10	2.10	0.50	0.50	1.60
1.70	4	6.80	1.57	0.50	2.00	4.80
1.30	7	9.10	0.77	0.50	3.50	5.60
1.00	10	10.00	0.30	0.50	5.00	5.00
0.50	13	6.50	-1.17	0.50	6.50	0.00
0.00	16	0.00	-2.17	0.50	8.00	-8.00

We can see that MR>MC for output level of 7 units but MR<MC for output level of 10 units.

Optimal output is 7 units.

Please refer above table for Q=7,

Corresponding price is $1.30

Corresponding profit is $5.60