Math Problem Solver

Question 1

Given the demand and supply functions for three interdependent commodities:

Qd1= 45-2P1+2P2-2P3

Qd2= 16+2P1-P2+2P3

Qd3= 30-P1+2P2-P3

Qs1= -5+2P1

Qs2= -4+2P2

Qs3= -5+P3

Calculate the equilibrium price and quantity of the above three – commodity market

model. [25]

Question 2

2.1. Given: 𝑇𝑇𝑇𝑇=2𝑞𝑞2+5𝑞𝑞+1800, show that MC curve lies above the AC when q >30

[5]

2.2. Consider the following Cobb-Douglas production function

�

�𝑄=15𝐾𝐾0.375𝐿𝐿5 8 �

Find

i. 𝑀𝑀𝑀𝑀𝐿𝐿 (4)

ii. 𝑀𝑀𝑀𝑀𝐾𝐾 (4)

iii. Calculate and comment on the returns to labour. (3)

iv. Calculate and comment on the returns to capital. (3)

v. Find the cross partial derivative of the Cobb-Douglas production function. (6)