# 1. Given production function Q = 0.30.7 (a) Use the lagrangian method to find the minimum cost of production.

^{}^{}while the price of labour is 3 and the price of capital is 5 and the maximum output that can be produced by the firm 250.

(b) Use the lagrangian method to find the maximum output.

2. Given output Q = LK -0.8K^{2} - 0.2L^{2} and the value of K=10.

a. Find the new production function given K = 10.

b. Find the expression for marginal product of labour.

c. Find the definition for marginal product of capital.

d. Find the expression average product of labour.

e. Find the level of output that equates average product of labour and marginal product of labour.

3. Determine whether the following functions exhibit increasing returns, constant returns and decreasing returns to scale and determine the degree of homegeneity

i. Q = 200 0.4 0.6

ii. Q = 200 + 2K +4L

iii. Q = LK -0.8K2 -0.2L2

4. Assume the production function for bread is Q= KL^{2}, with the price of capital and labor fixed at k10 and k15 respectively.

What combination of capital and labour minimizes the cost of producing 10,000 loaves? Find this minimum cost(USE the lagrange method)

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