a. A two-commodity market model is defined by:

Qd₁ = 4 - P₁ + 0.5P₂ .................1

Qd₂ = 8 +2P₁ - 2P₂ ......................2

QS₁ = - 5/2 + 3/2P₁........................3

QS₂ = - 3 + 6P₂ ........................4

Determine the equilibrium prices and quantities for the two commodities and the price and cross elasticities of demand and interpret their coefficients.

b. Suppose a firm operating in short run production and producing Metal rods faces a Cobb Douglas function of the form: Q= 600K²L² - K³L³ . Suppose capital is fixed at 10 units.

i. Compute the labour input that ensures that the largest possible number of Metal rods will be produced and how many Metal rods are produced at this labour input.

ii. Suppose management of the firm disregards the labour input computed in a above and decides to do the following.

Produces by 5 (five) fewer workers below the optimal.

Produces with 5 (five) more workers above the optimal.

Produces with 10 (ten) more workers above the optimal.

In all the three cases explain the consequences of such an action on the production of metal rods and clearly show in each case how produced has changed.

iii. Suppose each metal rod is sold at sh. 150. In each of the three cases listed in ii above show the impact on the firm's revenues.

iv. Compute the labour unit at the point where the Average Product of labour (AP_L) is at a Maximum and the number of Metal rods produced at that point.

v. Comparing the average productivity at the point where AP_L is at a maximum and MP_L is equal to zero, which of the two has the higher average productivity, by how much and why?