Question

Please solve the following show the work:

1. The generalized demand and supply functions for a certain good are determined to be:

Q_d = 800 – 2P – 0.01M + 16P_R

Q_s = 50 + 4P – 40P_I + 51F

1. Good X is a(n)_________good. Goods X and R are _____.

2. Suppose income is initially $20,000, the price of good R is $10, the price of the input (P_I) $25, the number of firms producing good X (F) is $20. Write the equations for demand and supply curves, where P is the only independent variable. Graph the demand and supply curves.

3. Find the equilibrium price and quantity.

Answer 1

Q_d = 800 – 2P – 0.01M + 16P_R

Q_s = 50 + 4P – 40P_I + 51F

Here:

Quantity demand for good X is inversely related to the income(M) that is as income(M) increases demand for good X decreases. It implies good X is an inferior good.

Quantity demand for good X is positively related to the price of good R that is as the price of good R increases the demand for good X increases. So it implies that good X and good R are substitute goods.

a. Good X is a(n) inferior good. Goods X and R are Substitute goods.

a. Suppose income is initially $20,000, the price of good R is $10, the price of the input (P_I) $25, the number of firms producing good X (F) is $20.

Q_d = 800 – 2P – 0.01(20000) + 16(10)

Q_d = 800-2P-200+160

Q_d = 760-2P Demand curve

Q	0	760
P	380	0

Q_s = 50 + 4P – 40(25)+ 51(20)

Q_s = 50+4P-1000+1020

Q_s = 70+4P Supply curve

Q	70	470	870
P	0	100	200

a. Equilibrium condition:

Q_d = 760-2P

Q_s = 70+4P

Demand = Supply

760-2P = 70+4P

760-70 = 4P+2P

690= 6P

P= 690/6= 115 Equilibrium price

Put P= 115 in supply curve:

Q= 70+4(115)= 70+460= 530 Equilibrium quantity