Assume that you can spend a budget of 1850 on two products

Question

Question 1: A monopolist has fixed costs (FC) equal to $250, and its total costs (TC) are given in Table. The (inverse) demand curve it faces in the market is described by this equation: P = 600 - (11.62)Q.

(a) Derive the MC and ATC values using the equation MC = ΔTC/ΔQ and ATC = TC/Q.

(b) Draw the MC and ATC curves using the values derived for 1(a). Draw the inverse demand curve and its corresponding MR curve. Note: for the MR curve, be sure to use the equation learned in class, MR = a - 2bQ.

(c) What is the price (P_M) and quantity (Q_M) that the monopolist will choose in order to maximize profit? What is their total profit from this price and quantity combination?

(d) What is the consumer surplus when they charge the price P_M from 1(c)?

(e) If the monopolist is able to price-discriminate and charge two different prices, P₁ = $251.40 and P₂ = $425.70, then what is their resulting profit? What is the consumer surplus under this price-discrimination?

Table 1: Total Costs for a Monopolist
Q	TC		Q	TC
0	250		31	2898.64
1	387.04		32	2968.72
2	518.32		33	3040.48
3	644.08		34	3114.16
4	764.56		35	3190
5	.880		36	3268.24
6	990.64		37	3349.12
7	1096.78		38	3432.88
8	1198.48		39	3519.76
9	1296.16		40	3610
10	1390		41	3703.84
11	1480.24		42	3801.52
12	1567.12		43	3903.28
13	1650.88		44	4009.36
14	1731.76		45	4120
15	1810		46	4235.44
16	1885.84		47	2355.92
17	1959.52		48	4481.68
18	2031.28		49	4612.96
19	2101.36		50	4750
20	2170		51	4893.04
21	2237.44		52	5042.32
22	2303.92		53	5198.08
23	2369.68		54	5360.56
24	2434.96		55	5530
25	2500		56	5706.64
26	2565.04		57	5890.72
27	2630.32		58	6082.48
28	2696.08		59	6282.16
29	2762.56		60	6490
30	2830

Question 2: Assume that there are four consumers (A, B, C, and D), each with their individual maximum willingness to pay for a product. Assume that there are four sellers (W, X, Y, and Z), each with a minimum price at which they are willing to sell. These reservation prices are given in Table 2 below. Assume that each seller has one unit to sell and each buyer only wants to buy one unit.

Consumers	Willingness to Pay	Sellers	Willingness to Sell
A	$80	W	$30
B	$75	X	$45
C	$65	Y	$55
D	$55	Z	$70
Table 2: reservation Prices of Four Buyers and Four Sellers

(a) If the price in the market was $60, which consumers would buy? How much surplus would each consumer get?

(b) If the price in the market was $60, which sellers would be willing to sell? How much surplus would each seller get?

(c) If the price in the market was $68, would the total surplus be greater than when the price was $60?

(d) If you could match buyers and sellers in order to maximize the number of units ex-changed, then buyers and sellers should be matched? What would be the total surplus resulting from these matches?

Question 3: Assume that you can spend a budget of $18.50 on two products, Apples and Bananas. The price of apples (P_A) is $1.75 per quantity and the price of bananas (P_B) is $2 per quantity. The marginal utilities of successive quantities of each is provided in Table 3.

MU(QA)	QA		MU(QB)	QB
14	1		15	1
13	2		13.6	2
12	3		12.2	3
11	4		10.8	4
10	5		9.4	5
9	6		8	6
8	7		6.6	7
7	8		5.2	8
6	9		3.8	9
5	10		2.4	10
4	11		1	11
Table 3: Marginal Utilities for Apples and Bananas

(a) Derive the marginal utility per dollar for each quantity of apples and bananas.

(b) What is the optimal consumption bundle (Q_A, Q_B) of apples and bananas?

(c) What is the MRS at the optimal consumption bundle?

(d) Is the optimal consumption bundle on the budget constraint? Graph the budget constraint and indicate the location of the optimal consumption. (Be sure to put QA on the horizontal axis.)

(e) What is the slope of the budget constraint?