Microeconomics: Understanding Prices and Markets - Essay Example

1. AC = MC = 10

Market demand curve: Q = 60 – P

To calculate the profit maximizing price and quantity combinations of the firm;

For a monopolist, for profit maximization, MR = MC (Krugman & Wells, 2005). Therefore,

P = 60 – Q

TR = PQ; TR = (60 – Q)Q

TR = 60Q – Q2

Finding MR, MR = dTR

                                 dQ

                      MR = 60 – 2Q

Therefore, π is given when MR = MC. So,

60 – 2Q = 10;             - 2Q = - 50

Q = 25            P = 60 – Q;     P = 60 – 25;    P = 35

Therefore, the profit maximizing price (P) = 35, while profit maximizing quantity (Q) = 25.

π = (P - AC). Q or π = TR- TC;       π = (35 x 25) – (25 x 10) = 625

Hence, the firm’s profits become: 625.

1. This is the case of when the market demand curve becomes steeper.

Q = 45 – 0.5P

0.5P = 45 – Q;            P = 90 – 2Q

AC = MC = 10;          TR = PQ;        TR = (90 – 2Q).Q;     TR = 90Q – 2Q2

MR = dTR

dQ

MR = 90 – 4Q

For profit maximization, MR = MC; 90 – 4Q = 10; -4Q = -80; Q = 20.

Finding P;       P = 90 – 2Q;   P = 90 – (2 x 20) = 50

Therefore, the profit maximizing price (P) = 50, while profit maximizing quantity (Q) = 20.

The profit becomes: π = TR- TC;     π = (50 x 20) – (20 x 10) = 800

Hence, the firm’s profits become: 800

1. Now, when the market demand curve becomes flatter, Q = 100 – 2P

2P = 100 – Q;                         P = 50 – 0.5Q;

AC = MC = 10;          TR = PQ;        TR = (50 – 0.5Q).Q;  TR = 50Q – 0.5Q2

MR = dTR

dQ

MR = 50 – Q

For profit maximization, MR = MC; 50 – Q = 10;   -Q = - 40;        Q = 40

Finding P;       P = 50 – 0.5Q;            P = 50 – (0.5 x 40) = 30

Therefore, the profit maximizing price (P) = 30, while profit maximizing quantity (Q) = 40.

NB: In these three scenarios, the inverse elasticity rule is explicitly illustrated (Perloff, 2004).

Question 2

1.  
2. When the price of ice cream decreases.

Inferior good- the price of other goods increases

1. I disagree with her. This is because; this gardener does not take into account the opportunity costs with the intention of going into growing the produce. She also requires taking into account her time spent in that garden even though she is not being paid a wage (Sobel, 2009).

The budget constraint from the information provided regarding income and prices of the two commodities becomes (Sobel, 2009),

100 = 5CC + 4SA

The slope of the budget constraint becomes,

- PSA / PCC = -4/5

Setting the two slopes equal to each other (Dolan, 2006), i.e. slope of utility function and slope of the budget constraint equal,

-4/5 = - (10/SA) / (2/CC)

- 4/5 = - 10CC/2SA

-8SA = -50CC

Eliminate the negative sign by dividing it by itself into both sides of the equation and we get (Dolan, 1977),

8SA = 50CC

SA = (50/8)CC;          Therefore, SA = 6.25CC

Using this value then to substitute it in the budget constraint we get,

100 = 5CC + 4SA

100 = 5CC + 4 (6.25CC)

100 = 5CC + 25

100 = 30CC:   Therefore, CC = 3.33

Finding the value of SA;        SA = 6.25CC;             SA = 6.25 x 3.33; SA= 20.8125

Therefore, from these calculations, we find that the number of pints of Samuel Adams Beer and bowls of clam chowder that will maximize the Senator’s utility over the next week is:

            SA = 20.8125 and CC = 3.33