Question

9.         Suppose the following set of simultaneous equations represents the demand and supply functions for Beef (B) and Chicken (C) fillets in the Barbecue market:

For Beef:         Qd_B = 82 – 3P_B + P_C

                        Qs_B = -5 + 15 P_B

For Chicken:   Qd_C = 92 + 2P_B – 4P_C

                        Qs_C = -6 + 32P_C

Find the equilibrium conditions (price and quantity) for each product.

10.       The Table below shows the Total Utility (TU) and Marginal Utility (MU) derived from the consumption of 10 units of the commodities X and Y.

a. Derive a column for the Marginal Utility of x (MU_x), and a column for the Total Utility of y (TU_y).

                        b. On separate graphs, plot the Total and Marginal curves for each commodity, placing the panel of the marginal utility curve below the panel for the total                                          utility curve for each commodity.

                        c. Determine at what unit of each commodity a consumer reaches the point of saturation, and mark it on both the table and graph for each.

                        d. Describe the behavior of both curves for each commodity based on your observations of the slopes.

                        e. At what unit a consumer reaches equilibrium if he buys both commodities when their prices are:

                       

                                                P_x = $2 and P_y = $1.

                       

                        f. What must be the consumer budget, which he spends entirely on the two commodities?

Q	TUx	MUx	TUy	MUy
0	0			0
1	7			4
2	13			10
3	18			8
4	22			6
5	25			4
6	27			2
7	27			0
8	26			-1
9	25			-2
10	23			-3

                       

11.       If the Total Utility function for product x is given by:

TU = 1000 Q_x – 2Q²_x

            At what quantity of x a consumer will reach the point of saturation?

Answer 1

Question 9

BEEF

QdB = 82 - 3PB + PC

QsB = -5 + 15PB

In equilibrium,

QdB = QsB

82 - 3PB + PC = -5 + 15PB

-3PB - 15PB + PC = -5 - 82

-18PB + PC = -87

PC = 18PB - 87                  ...Equation (1)

CHICKEN

QdC = 92 + 2PB - 4PC

QsC = -6 + 32PC

In equilibrium,

QdC = QsC

92 + 2PB - 4PC = -6 + 32PC

2PB - 4PC - 32PC = -6 - 92

2PB - 36PC = -98

Put value of PC from Equation (1) in above equation,

2PB -36(18PB - 87) = -98

2PB -648PB + 3,132 = -98

-646PB = -3,230

PB = 3,230/646 = 5

PC = 18PB - 87 = (18*5) - 87 = 90 - 87 = 3

So,

For Beef,

Equilibrium price, PB = $5

Equilibrium quantity, QB = 82 - 3PB + PC = 82 - (3*5) + 3 = 70

For Chicken,

Equilibrium price, PC = $3

Equilibrium quantity, QC = 92 + 2PB - 4PC = 92 + (2*5) - (4*3) = 90

Question 11

A consumer reach the point of saturation when he consumes that quantity of a commodity corresponding to which marginal utility is zero.

TU = 1000Qx - 2Q²x

Calculate marginal utility -

MU = dTU/dQx = d(1000Qx - 2Q²x)/dQx = 1000 - 2Qx

Put MU equals to zero

MU = 0

1000 - 2Qx = 0

2Qx = 1000

Qx = 500

So,

A consumer will reach point of saturation when he consumes 500 units of x.