Question

1. A restaurant faces very high demand for its signature mousse desserts in the evening but is less busy during the day. Its manager estimates that inverse demand functions are pe = 34 - Qe in the evening and pd = 24 - Qd during the day, where e and d denote evening and daytime. The marginal cost of producing its dessert evening, MCe, is $8. The marginal cost of producing its dessert daytime, MCd, is $4. There is no fixed cost of producing dessert.

Create a spreadsheet with the column headings Qe, Pe, TRe, MRe, TCe, MCe, πe, Qd, Pd, TRd, MRd, TCd, MCd, and πd. (note: πe is profit evening and πd indicates profit daytime)

What is the optimal prices for the dessert that the restaurant should charge during the evening hours? __________

What is the optimal quantity for the dessert that the restaurant should produce during the evening hours? __________

What is the total cost of producing the optimal quantity for the dessert during the evening hours? __________

What is the maximum profit for the dessert that the restaurant should produce during the evening hours? __________

What is the optimal prices for the dessert that the restaurant should charge during the daytime hours? __________

What is the optimal quantity for the dessert that the restaurant should produce during the daytime hours? __________

What is the total cost of producing the optimal quantity for the dessert during the daytime hours? __________

What is the maximum profit for the dessert that the restaurant should produce during the daytime hours? __________

QUESTION 2

1. A monopoly sells its good in the U.S. and Japanese markets. The American inverse demand function is P_A =60−Q_A, and the Japanese inverse demand function is P_J =80−2Q_J, where both prices, P_A and P_J, are measured in dollars. The firm’s total cost of production is TC=5+16Q in both countries. Assume that the firm can prevent resale in other countries.

   What price will it charge in the U.S.? ________

   What is the optimal quantity in the U.S.? ________

   What is the total cost producing the optimal quantity in the U.S.? ________

   What is the maximum profit for the good in the U.S.? ________

   What price will it charge in the Japanese markets? ________

   What is the optimal quantity in the Japanese markets? ________

   What is the total cost producing the optimal quantity in the Japanese markets? ________

   What is the maximum profit for the good in the Japanese markets? ________

   Now, resale is allowed in both markets. What is the optimal price in both markets (round to the nearest whole number? ________

   What is the optimal quantity in both markets? ________

Answer 1

Qe	Pe	TRe	MRe	TCe	MCe	πe	Qd	Pd	TRd	MRd	TCd	MCd	πd
0	34	0		0		0	0	24	0		0		0
1	33	33	33	8	8	25	1	23	23	23	4	4	19
2	32	64	31	16	8	48	2	22	44	21	8	4	36
3	31	93	29	24	8	69	3	21	63	19	12	4	51
4	30	120	27	32	8	88	4	20	80	17	16	4	64
5	29	145	25	40	8	105	5	19	95	15	20	4	75
6	28	168	23	48	8	120	6	18	108	13	24	4	84
7	27	189	21	56	8	133	7	17	119	11	28	4	91
8	26	208	19	64	8	144	8	16	128	9	32	4	96
9	25	225	17	72	8	153	9	15	135	7	36	4	99
10	24	240	15	80	8	160	10	14	140	5	40	4	100
11	23	253	13	88	8	165	11	13	143	3	44	4	99
12	22	264	11	96	8	168	12	12	144	1	48	4	96
13	21	273	9	104	8	169	13	11	143	-1	52	4	91
14	20	280	7	112	8	168	14	10	140	-3	56	4	84
15	19	285	5	120	8	165	15	9	135	-5	60	4	75
16	18	288	3	128	8	160	16	8	128	-7	64	4	64
17	17	289	1	136	8	153	17	7	119	-9	68	4	51
18	16	288	-1	144	8	144	18	6	108	-11	72	4	36
19	15	285	-3	152	8	133	19	5	95	-13	76	4	19
20	14	280	-5	160	8	120	20	4	80	-15	80	4	0
21	13	273	-7	168	8	105	21	3	63	-17	84	4	-21
22	12	264	-9	176	8	88	22	2	44	-19	88	4	-44
23	11	253	-11	184	8	69	23	1	23	-21	92	4	-69
24	10	240	-13	192	8	48	24	0	0	-23	96	4	-96
25	9	225	-15	200	8	25	25	-1	-25	-25	100	4	-125
26	8	208	-17	208	8	0	26	-2	-52	-27	104	4	-156
27	7	189	-19	216	8	-27	27	-3	-81	-29	108	4	-189
28	6	168	-21	224	8	-56	28	-4	-112	-31	112	4	-224
29	5	145	-23	232	8	-87	29	-5	-145	-33	116	4	-261
30	4	120	-25	240	8	-120	30	-6	-180	-35	120	4	-300
31	3	93	-27	248	8	-155	31	-7	-217	-37	124	4	-341
32	2	64	-29	256	8	-192	32	-8	-256	-39	128	4	-384
33	1	33	-31	264	8	-231	33	-9	-297	-41	132	4	-429
34	0	0	-33	272	8	-272	34	-10	-340	-43	136	4	-476

TRe = Pe*Qe = (34 – Qe) *Qe = 34Qe – Qe^2

MRe = dTRe/dQe = 34 – 2Qe

At equilibrium:

MRe = MCe:

34 – 2Qe = 8

2Qe = 26

Qe = 26/2 = 13.

Optimal Price from Demand curve:

Pe* = 34 – 13 = 21

Optimal quantity Qe* = 13.

Total cost of producing this quantity TCe* = 8*Qe*= 8*13 = 104.

Maximum profit = TRe – TCe = 13*21 – 8*13 =169.

During Day time:

MRd = dTRd/dQd

TRd = (24 – Qd)*Qd = 24Qd – Qd^2

MRd = 24 – 2Qd

Equilibrium:

MRd = MCd

24 – 2Qd = 4

2Qd = 20

Qd* = 10.

Optimal price from demand curve:

Pd* = 24 – 10 = 14

Optimal quantity: Qd* = 10.

Total cost = MC*Qd* = 4*10 = 40

Profit πd = TRe – TCe = 14*10 – 40 = 100

Hi. Please post questions separately.